Uploaded by GoogleTechTalks on 28.10.2010

Transcript:

>>

Good afternoon everybody. Welcome back. I think the only qualification I have for during

the session is I'm the only one in the building with a tie on, so. That's a reason. Anyway,

I'd like to introduce this afternoon, Elisabeth Rieper from National University of Singapore

Centre Quantum Technology. She's going to talk about Classical and Quantum information

in DNA. Thank you. >> RIEPER: Yes. Hello everybody. First of

all, I would like to thank Google for organizing this really cool workshop. And yes, I will

talk a lot about information and going to Google and to talk about information feels

very interesting. Okay, I know a little bit about quantum mechanics. So, first of all,

I will spend a couple of slides to--to explain the title in detail and then very briefly,

I will talk about decoherence, then all those concepts developments, the first section will

be applied to--to DNA. And then the really interesting part is the quantum matter. I

can say it right now, I do not know, but I will make some speculations. And then finally,

I will compare those different computing structures like classical computers, DNA, and quantum

computers and show where they are similar and where they differ. Quantum biology suffers

from one severe problem, namely is that biology is a massively complex system, whereas quantum

mechanics is massively deep. So if you change a little bit like we've seen with the talk

from Luca Turin, suddenly everything changes. So combining this complexity with the deepness

is a challenge. So for--for combining quantum information concepts with DNA, I have to do

some simplifications and I apologize to any biologist if those simplifications turn out

to be too brutal, details really matter. So what is DNA? Let's start with the Wikipedia

definition of that. So it's a deoxyribonucleic acid. So it's a nucleic acid that contains

genetic instructions used in the development and functioning of all living organisms. The

main role of DNA molecules is the long-term storage of information. So the last sentence

that sounds rather innocent, actually contains two very interesting concepts. So, the first

concept is information and the other one is long-term storage. So what does it mean long-term

storage? It means that we have some information, whatever information is, in the past and we

would like to send this information into the future. That's long-term storage. And the

way we send it from past to future can be described by a channel. And a channel is a

very general description of whatever happens to your information. So, what is information?

Well, I already asked this question to Google. That was the answer. It came pretty quickly

and it's got a lot of results, but I actually did not bother to read all those results.

So, as a consequence, I will give you a couple of my--my own definitions, what I like to

think about information. First of all, you can see it as negative entropy. So now I want

into the problem so I have to explain to you what is entropy. Entropy, in general, measures

the ignorance you have about the system. If your system has zero entropy, you know everything

about it. You have maximum information. If your entropy is large, there are certain things

you don't know about it and you have few information. And entropy is a well structured--established

concept and information theory. So how do you use it? You choose an alphabet. That could

be computational bases of two or one or anything else. Then in the next step, according to

that alphabet, you count probabilities. And once you have that probability distribution,

you can calculate the entropy of your choice. There's a whole family of it. Here, I've shown

you the [INDISTINCT] entropy which is widely used and very useful. But, I'm a physicist

and we can do the same in statistical physics. In that case, we choose our system of interest

and then we count the number of possible states which is denoted by capital omega, and then

we take the [INDISTINCT] of set number and KB as a constant--don't care too much about

the meaning. The massively interesting thing is that once all events are equally likely,

those two definitions of entropy actually coincide. This is one of the many links between

information theory and physics. So it sounds like combined science and then something different.

And in physics, we have the well-established second law of thermodynamics and that tells

you that in closed system, entropy does not decrease. So if we translate that argument

to information theory, we immediately know that in closed system, information cannot

increase spontaneously. That's very important to know. Next thing I would like to point

out that information is physical. Whenever you have a piece of information that comes

together with the physical carrier that can be the piece of paper you are writing now

at the moment, or it can be your hot wife on the computer. And for classical physics--for

classical information, we know from everyday life, I can change that information carrier.

I can write something on a piece of paper, I can scan it to my computer and I can print

it again. And if I didn't do obvious mistakes, I didn't lose any information. So that--that's

allowed by laws of classical physics, but as information comes along with the classical

carrier, the way I process information is bound to the laws of physics. So what happens

if I choose my physical carrier to be smaller and smaller until I reach the quantum limit?

Then the fascinating thing is the way I process information changes, according to the laws

of quantum mechanics. So what does that mean? So one thing is set, I cannot copy quantum

information, I can only copy classical information. And whereas classical information reliably

stores the information, in quantum mechanics, I always have to find decoherence. It's always

getting lost. So, coming back to the problem of DNA to use a long term storage, what I

just told you was those two points would actually mean that quantum mechanics is not any good

for DNA and if you really want to store your genetic information safely, you should keep

away from quantum mechanics. So what is the good point of it? Quantum mechanics allows

you to do more, and classical mechanics is a special case, and only has a certain set

of manipulations and quantum gives you more. So, now the question is, does nature exploit

this edge of being able to do more? Just a very short reminder of the notation, if you

have a classical bit, that's usually denoted by zero or one. If you have a quantum bit

or a QuBit, you put the zero and one in these brackets, as we call them [INDISTINCT]. And

I have one interesting feature, it sets a--sorry--that allows superposition. So in the classical

case, you have to decide whether the QuBit is zero or one. But in the quantum case, you

can combine it in a superposition. And then you have a mixture where the bit--the QuBit

is either zero or a one. You just don't know which one it is. So in superposition, it is

both simultaneously and in the mixture, you don't know which one it is. So I told you

that you cannot copy quantum information. The proof is this three-liner. So let us suppose

you could copy quantum information. Then you would have some--some unitary acting on your

way function-side so that actually copies an unknown state to your template. And then

I can suppose that that's [INDISTINCT]. It's a superposition of zero and one and I plug

it into the formula and I get that lengthy expression of the copied state, but the mathematical

formula of quantum mechanics also allows me to feed it in step by step. So I can feed

in first as Peter get one part which is copied to one one and then the alpha zero part which

is copied to alpha zero. That should be the same but we can see clearly it's not the same.

So assumption, is that we can copy quantum information was actually wrong and that's

causing the cloning theory. Actually, there was one special case where these two lines

are the same, namely Aiza, Alpha, beto or zero. And this tells you, which would roughly

correspond to classical information, so that's something you can copy. And another thing

I would like to mention in my introduction, is conditional entropy. So the conditional

entropy measures how much uncertainty, how much ignorance you have about a combined system

and observer and given that you have all of the observer's knowledge. And for anything

that we encounter in the real world, there's a fair assumptions that this conditional entropy

is bound to be low by zero. So the idea is that if my observer has a certain ignorance

about his own state, then the combined system and observer should have at least this uncertainty.

So but if we--if we are now dealing with this state, as was mentioned before this morning,

actually, I have full knowledge about the full system. I--globally, I don't have uncertainty,

but if I look at the state, the observer himself has, he actually has uncertainty. So this

quantity for quantum systems, this conditional entropy can actually be smaller than zero.

And whenever something like this happens, we call it entanglement. So whatever physical

meaning entanglement has, you can take it as very strange probability distributions

which allow you to--to achieve correlations which are classically not possible. So one

application, let's suppose you have a system which is in a mixture of zero and one. And

you would like to reset, it could be for example your memory, and you would like to reset that

to--to state zero. And what is usually called [INDISTINCT] state, is that a classical observer

has to pay one unit of work to extract or to erase that information. Is it any different

if we are dealing with the quantum observer? Yes. It could be that the quantum observer

actually has the other half of a maximally entangled state and then the system has the

same correlations. As was shown recently, in that case, you can actually extract one

unit of work and you erase information to reset it to zero. And now, we are talking

about biology. Whatever small enzymes, molecules and other systems are wiggling around in your

biological systems, it could be that it's small enough to be a quantum observer. And

then suddenly, the whole set up changes. Instead of needing to pay work, you can actually extract

work and you can do the same. So it might be that for those small biological systems,

we need to change the way we think about it. And another thing I would like to mentions

is, information is a subject of quantity. It depends on the knowledge you can have.

And that might be different for different observers. So, this was the introductions.

It was a lot of concepts. That's the only slide I will mention about decoherence. You

can talk a lot about it, but I will abbreviate it to the time a system can maintain its quantum

coherence. It's roughly inverse proportional to the mass and the temperature. So why don't

we see any quantum effect on the real life? We are massive. We have a lot of mass, and

the second reason is we are hot. We are at 300 Kelvin, that's a lot of temperature. So,

whenever you have these two effects, you would believe that you don't have quantum effects.

So finally, information in DNA. So, probably most of you already know this molecule. Let

me just give you a brief reminder. So, this DNA is this really single long molecule. And

outside here, you have some phosphate that bound into sugar stabilizing, so DNA. But

it's actually--those four nuclide acids that contains a genetic information. And when I

first looked at it, it's those molecules, I thought, "Well, they are pretty small compared

to our computers, what we encode in a bit in a computer." And because here we are--we

have four different bases, each molecule encodes two bits. Yes, and then these two bits are

arranged in a linear, away into the two--two ends have opposite information. Now, the interesting

question is, how do you actually access that information? It's not enough to store with;

you actually have to be able to read it out. How do you do that with these small systems?

So, let's look at only one of them, cytosine for example. So, that's for you on the right

side, isn't it? No, that's for you on the left side. So on the left side, it's actually

bound to the phosphate backbone, so you cannot access it. Up and down of this cytosine here,

you have electron clouds and other nuclide acids, so you cannot access that part either.

So, the only part where you can actually access that molecules is on the right side. So--and

this is actually what's used in biology. Here we have those atoms, that's Nitrogen and Oxygen;

and single protons can bind to it. So now, the idea is to use acquisition of those protons

to encode the identity of that molecule. Another thing I should mention is, that this aromatic

ring you see there, that's actually--even though I consider it small, for quantum mechanics,

it's actually quite large. So this is something we can safely assume to be classical information.

Whereas the position of a single proton, a single proton is due to loss of quantum mechanics,

that might tunnel. So, this leads me to this notation that's a little bit sloppy but it's

good for transferring ideas. So, the classical information that we are dealing with--since

the molecule cytosine is something I would encode in this quantum state which means that

the lower two slots where the proton could be empty, and the upper slot is filled; so

that's denoted by those zeros and ones. So, then how do you--how do you combine it? Cytosine

always pairs with Guanine and so Guanine has the opposite slot, so the lower two slots

are filled and the third one is empty. And then, when you bring those two molecules together,

you can form H bonds. And you can only have one proton in these H bonds; so that's why

it's necessary to have this sort of matching proton distribution. So here, it's really

a lock-and-key mechanism. Same holds for Thymine and Adenine. So, does this mechanism work

perfectly? No. What can happen is that here your cytosine goes into its rare form, which

means that its proton tunneled to the second slot; that's allowed you to do quantum mechanics.

But then, when we go to the look-up table of the encoding, so it actually looks the

same like a Thymine. And as a consequence, because the quantum information pretends that

this molecule is a Thymine, the Adenine thinks that it can bind to it; and that's one way

of how you can get mutations to your system. So, once again, you have here a classical

bit which you encode in this quantum information, and epsilon is some sort of a tunnel probability.

So, epsilon is small. So most likely, it stayed in this state, you encoded it. But there was

a small probability that your quantum information was--test-wide into a different state. So,

this is quantum information into transversal direction. So, let's make a little jump to

the longitudinal direction. All these--these nuclide acids, they are more less plan a molecules

being surrounded by electron clouds. These electron clouds, because you're dealing with

aromatic rings, are highly delocalized; so that's why I draw them in such a sandwich

notation. So now, what happens is that these electron clouds carry negative charge. And

we know that adjacent negative electron clouds will repel each other. The intriguing thing

is that this actually leads to correlated excitations lowering the ground state energies.

So, different charged clouds kick each other, and then they redistribute their charged distributions;

and that can actually lower the ground state energy. Now, that effect is called Van der

Waals interaction or Van der Waals forces. And you actually need the coherence between

neighboring sites to get the attractive part of the force. But now, this is also has nontrivial

implications. So, first of all, neighboring sites are entangled due to these continuous

interactions. And also, the electron cloud of one site carries information about the

identity of the other site. So, if I'm a Thymine here, and I'm adjacent to an Adenine, this

Adenine influences my own electronic state. If there would be a cytosine next to me, my

own state would look different; and that's substantially different from classical computing.

So, my own identity is influenced by the neighbors I have in the DNA chain. Now, I just gave

you two examples where you can expect quantum information to be present in DNA. And maybe

the one or other just was irritated because we are room temperature-systems. So, how does

it work together that I told you, if you have massive hot systems at room temperature, you

cannot have entanglement. Well, I didn't tell you everything, details matter. So, you can

analyze a very generic model of couple thermal oscillators. And then you actually see that

the absolute temperature does not matter. It's a temperature, so kBT, the thermal energy

compared to the interaction energy that matters. And if that coefficient is small, then you

can expect quantum effects to be present. And if you pluck in all the numbers we have

for this longitudinal entanglement, you see that thermal energy is actually very small

compared to the interaction energy. So DNA has optical frequencies; and this means that

the thermal noise cannot excite those optical frequencies. So, this quantum information

we are talking about is basically in its ground state, even at 300 Kelvin. So, here was a

screenshot from a computer program where you do something with DNA; you've seen it many

times before. And to sum it all up, what I told you at the previous slides, everything

that you can see on this picture is classical information. The black stuff and the double

helix that you cannot see, that's a quantum information. So, they--I haven't discovered

any good way how to--how to picture correlations. Probably, there was no way; so that's why

nobody ever draws quantum information. But the next time you see such a double helix,

you know, okay, all the stuff I do not see, that's a quantum information. So basically,

what happens is this classical information by which is usually drawn here is embedded,

is sandwiched into quantum information. And most likely, this classical information is

never accessed; you can only--because it's inside--all the quantum information, you can

only access the quantum information or the electron clouds and the protons. So mathematically,

you can describe that as a quantum-classical state. So, let's suppose that X is a string

of classical symbols; you would denote that the state has two components. So the first

one denotes the classical information, this is diagonal and its basis has no coherence.

But this actually comes along with some sort of quantum information. And so, X for example,

could be the string of your DNA; and then it is embedded in this cloud of quantum information.

And Paul Davies called this sort of quantum information, shadow information. Because in

this quantum information, you have at least one copy of the information in your DNA, if

not, more copies. And if you want to decode your classical information, you measure the

quantum part. But it can happen that the quantum part of science is not fully distinguishable,

and this gives possibility for mistakes. So, coming to the most important question, does

it matter at all? Well, I do not know for certain; but I think there are many things

quantum allows you to do. And if quantum gives you an advantage, this four billion IT project

probably discovered how to use it. Let me come back to the channel picture I introduced

in the beginning. So, you would like to send some classical information from the sender

to the receiver. We do it everyday. We send text messages, we send email, we talk; that's

also classical information which uses classical channels. The only problem is that this probably

doesn't take place in DNA; because the system you are talking about is too small to really

have a full classical channel. So it's more likely that you're dealing with a quantum

channel. You can send classical information in the quantum channel, that's no problem.

So you encode your classical information on your quantum system, you send your quantum

system, then you make a measurement on it and decode the information it carries. And

there are two channels I would like to compare: The normal quantum channel, and the entanglement

assisted quantum channel, where actually the sender and receiver initially share entanglement.

And then, I will talk about the capacity of channels. And this roughly measures how much

information can be transmitted in this channel. So that's a number between zero and one. If

it's one, you can fully transmit all the information you send in. And if it's zero, your channel

is useless and you cannot send any information. Calculating channel capacities is very, very

difficult; and those capacities are not known. But for some simple channels, they are known,

and one of them is called Qubit depolarizing channel. So, what happens here, you take your

way function, sign of X, and you send it to the channel. But it can actually happen, that

in this channel, it suffers from some sort of noise; as we can expect it with biological

systems. And then, with probability one minus epsilon, this channel gives you the original

way function; and with probability epsilon, it sends you something completely random.

So that's the Qubit depolarizing channel. And now, if you would like to encode your

classical information X, so X could be added into mean or whatever. You encode that in

a certain way function, you send it through your noisy channel, and with some probability,

you recover X. But in some cases, you guess incorrectly and you recover Y. So, how often

you guessed correctly and how often you guessed incorrectly, is characterized by this channel

capacity K1. And now, you can--you can use the same channel. The only difference is that

now, sender and receiver initially share maximally entangled states and so you have capacity

KE; E for entanglement. And the beautiful thing is if you use entanglement, you can

double your channel capacity. So, we have a system where you would like to transmit

classical information. It is reasonable to assume that you can create this entanglement

resources and this entanglement would allow you to double the capacity of your noisy channel.

So that's something we're thinking about. Something completely different, how you might

use entanglement in DNA is for communication along the chain. When I read up on the literature

on how little motors go along the DNA and achieve things, I always wonder what—how

does it work? How do these motors actually know what they are supposed to do? So let

us suppose that each of these balls represents a site in your DNA and what I do is I wiggle

the one end of it and then you can calculate what's happened to it. Actually, after some

time, you will get entanglement between the first side where you shake your end and the

nth side could be the 10's or 20's or 30's side along the chain. And suddenly, these

two far apart side share entanglement, and entanglement means it's a half correlation.

So the question is, can you use those correlations for communicating along this one dimensional

chain? And the next thing is something where my own ignorance comes up. I do not know too

much about protein folding but I have a background in Information Science so I would like to

ask a question to people who know more about Biology. So when I would like to fold a protein,

I start with my DNA, which is a one-dimensional sequence of information. So, in order to fully

describe my--the classical information in DNA, I only need to know this one-dimensional

sequence. Then I make a copy to RNA and the information content did not change. In the

next step, I translate pairs of [INDISTINCT] of my RNA into an amino acid. Now, there's

some sort of quote and quote, you might argue that you lost some information—-I'll ignore

that effect for the moment. And then it's a four step, this is one-dimensional chain

of amino acid, actually folds into a three-dimensional structure. So let's look at it again. You

start with DNA, messenger RNA and this chain of amino acids and because they are all linear

arrangements, I would argue that roughly up to small errors that can carry the same amount

of classical information. And then you fold a protein, and it's getting a three-dimensional

structure, and the shape is vital to its functioning. But now, you need to store more information.

In addition to the sequence, you have the position information and in my opinion, that's

actually an increase of information. But we also know from the second law that in closed

systems, information cannot increase spontaneously. Now I know that creating a protein is far

away from being a closed system but my question to the biologists is actually, "Where does

this additional information come from?" If you think about it in detail, that's actually

not that trivial. Does it come from the time sequence in which you assemble the protein?

Does it come from some sort of laws of quantum mechanics? Do you have some sort of quantum

information actually also taking place? If anybody can tell me, I'll be very happy. So,

[INDISTINCT] question that's actually taking from a German piece of literature, let's go

to Faust, it's a very nice book; I can only recommend reading it. And so it's sort of

an important question. So the important question is, does quantum information matter? And there's

one way to test it. So you take two identical strings of classical information and by some

means and one string, you change the quantum information. There are some ways to disturb

quantum information. And then you actually look—-does it fold in the same configuration

or does it fold differently? If two strings with the same amount of classical information,

but different quantum information fold into different chains—-into different configurations,

different shapes, that would actually be a good argument that quantum information matters.

And does this—-is this line of thought generalizes to other situations. When you wonder, does

quantum matter? Well, disturb it, shake it, destroy it, and see if it makes a change and

then you'll know if quantum matters. So, last point, comparing those different platforms

which all have to do with information flow. If I have a classical computer, I would initialize

it and either zero or one or any other computational basis. When the--for DNA, I argue that you

use quantum classical states and for quantum computing, I didn't talk too much about quantum

computing, so if you are unfamiliar with the subject, you can just ignore those in the

last column. You have whatever space your quantum computing is assigned to with its

Hilbert space. Then you let those bits attach and for classical computers, that should be

fairly independent. If I store a value of zero here, this is independent if next to

it is a zero or a one. For DNA, the value—-the quantum information of a single side strongly

depends on the quantum information on the next side. And for quantum computing entanglement,

it seems to be the crucial quantity, so then you fully exploit it as a non-local correlations.

With classical computation, you do gates like 'and', 'or', 'not' and many more. In quantum

computing, you have a universal set of unitary dates and I have to say that in DNA, I have

no idea what sort of gates are possible. That would also be interesting if--to work together

with someone in biology to actually classify the allowed operations on DNA. When it comes

to cutting DNA and reassembling, that's getting pretty loud. And also, non-equilibrium will

be the most interesting case. What I said about shaking one end and seeing how the correlation

spread along the chain, that's non-equilibrium. The gate time will be short for classical

and quantum computing. In classical computing, the shorter the date—-gate time, the faster

your processor works. For quantum computing, you always need to find the decoherence, so

that's why you have to make it short. DNA will be a bit—-a little bit different, because

you have this sort of continuous interaction. And then finally, the way out for a classical

computer that's purely deterministic and you make only a few errors. With quantum computing,

it's actually statistical. You need to repeat the same experiment many times before you

can actually have a read-out and DNA is again somewhere in the middle. So if you want to

read-out DNA information, you have a single shot, you have one try to do it. So given

all the quantum that's involved, I would actually like to know the accuracy of that read-out.

So, there's many, many more things you could compare but what you see already is that DNA

seems to sit somewhere in the middle between classical and quantum computing. So the conclusion

of this talk is that both classical and quantum information should be considered for full

understanding of DNA, even if DNA is probably not a full quantum computer. And there are

many people I would like to thank for, for help for discussions, for preparing this talk.

So, Mile Gu, Oscar Dahlsten, Kavan Modi, Giovanni Vacanti, Janet Anders, my supervisor Vlatko

Vedral and there are probably many more. And yeah, thank you for your attention.

>> I'll have the mic then. I have three questions, actually comments. The first is, I would like

to solve your problem. Actually, there's no information gained.

>> Yeah. >> Because you have to look at the entire

environment which includes water and this is a typical problem in protein folding. When

you include water, it's an entropic force, so you calculate all the energy and you minimize

your energy of the entire system, which is DNA with water or protein or peptize with

water, and you end up with equilibrium confirmation, which is the folded state, and that corresponds

to the minimum energy or maximum entropy. So, I mean, of course, we have to do detailed

calculations but I maintain that when you do that, you will end up with possibly a loss

of information, not gain of information. >> Of course, when you consider the whole

box, then of course, you cannot gain information, but still, I would like to understand how

this information from the water molecules actually...

>> No, it's very simple because water molecules attach to peptizer, I mean, acids and by doing

so, they lose information about their conformational freedom of movement. So free water molecule

has rotation degrees in transitional, when it's bound, it loses this freedom and that's—-it

can be quickly calculated entropy gain or information loss. The idea of the superposition

of quantum and classical wave function for the DNA, I think is a great one. And I think

you call this shadow information or something, but actually it can be made very concrete.

We think about DNA as the sequence of nucleotides, you know, the code. But actually, it's not

letters; these are molecules, they are vibrating. So the vibrating—vibrations around the bonds

are like wave functions. So this is really quantum-mechanical oscillations and that can

be your shadow, if you will. Because if you think about just the sequence, yes. And these

vibrations actually reflect the neighborhood. So what you talked about, the importance of

neighborhood, it's preserved by the nature of the vibrations. And finally, very quick,

the gates and the read-out, I think there's a whole slew of proteins like conscription

factors and DNA polymer razors--enzymes that participate in this and these are the readers

and the writers and the gates in all this. Anyway, that's all I have to say.

>> So, Eddie had mentioned [INDISTINCT] but [INDISTINCT].

>> Could you get up and speak louder? >> Yeah, okay. So, did you mention at all

why the quantum coherence could survive at room temperature for these DNA molecules?

>> Yes. So one pound of the quantum information is encoded in this electronic degree of freedom

and it just happened that you have optical frequencies for this system and your room

temperature cannot excite those optical frequencies, so that's why you are basically on the ground

state. Another thing is that you have this double helix and that's actually shields very

well and any noise from it. >> So you are saying this is-—this has nothing

to do with a non-equilibrium state of this DNA vibrational mode? So you are saying even

in a static form? >> Yes. So far, my calculations are only static

and the next step I will look at, at non-equilibrium. But even in static, you have a massively stable

system—-massively stable in the sense of maintaining quantum information because of

those optical frequencies. >> [INDISTINCT]

>> Well, with the proton tunneling, it's more delicate because you can only measure on one

basis and then it's actually undistinguishable whether you have a coherent superposition

or a mixture. But for tunneling to take place at some point, it needed to be a superposition,

that's why I denoted [INDISTINCT]. >> [INDISTINCT]

>> Unfortunately, I'm a physicist. I hope that some biologists in the audience can answer.

>> Yeah, because it is—-it goes to the comparison at the end that you did a table that you compare—-yeah,

classical computing DNA and quantum computing. I mean, I don't see any discussions of the

coherence [INDISTINCT] skills here. So I think... >> We can add it in the next coffee break.

>> Okay. >> Let us take one more question then we will

have a break. >> I think it's—-I mean there are lots of

experiments we know about that we show entanglement over space. Now, I wonder if you're suggesting

that there's entanglement over time with DNA sort of being the string between.

>> That's a slight misunderstanding from the notation I used. You can have entanglement

over time. Here, I do not propose it. It's that you have the classical information in

the past which you want to send into the future and each step might use quantum mechanics,

but that's a different problem. >> Okay, I'd like to thank our speaker one

more time please.

Good afternoon everybody. Welcome back. I think the only qualification I have for during

the session is I'm the only one in the building with a tie on, so. That's a reason. Anyway,

I'd like to introduce this afternoon, Elisabeth Rieper from National University of Singapore

Centre Quantum Technology. She's going to talk about Classical and Quantum information

in DNA. Thank you. >> RIEPER: Yes. Hello everybody. First of

all, I would like to thank Google for organizing this really cool workshop. And yes, I will

talk a lot about information and going to Google and to talk about information feels

very interesting. Okay, I know a little bit about quantum mechanics. So, first of all,

I will spend a couple of slides to--to explain the title in detail and then very briefly,

I will talk about decoherence, then all those concepts developments, the first section will

be applied to--to DNA. And then the really interesting part is the quantum matter. I

can say it right now, I do not know, but I will make some speculations. And then finally,

I will compare those different computing structures like classical computers, DNA, and quantum

computers and show where they are similar and where they differ. Quantum biology suffers

from one severe problem, namely is that biology is a massively complex system, whereas quantum

mechanics is massively deep. So if you change a little bit like we've seen with the talk

from Luca Turin, suddenly everything changes. So combining this complexity with the deepness

is a challenge. So for--for combining quantum information concepts with DNA, I have to do

some simplifications and I apologize to any biologist if those simplifications turn out

to be too brutal, details really matter. So what is DNA? Let's start with the Wikipedia

definition of that. So it's a deoxyribonucleic acid. So it's a nucleic acid that contains

genetic instructions used in the development and functioning of all living organisms. The

main role of DNA molecules is the long-term storage of information. So the last sentence

that sounds rather innocent, actually contains two very interesting concepts. So, the first

concept is information and the other one is long-term storage. So what does it mean long-term

storage? It means that we have some information, whatever information is, in the past and we

would like to send this information into the future. That's long-term storage. And the

way we send it from past to future can be described by a channel. And a channel is a

very general description of whatever happens to your information. So, what is information?

Well, I already asked this question to Google. That was the answer. It came pretty quickly

and it's got a lot of results, but I actually did not bother to read all those results.

So, as a consequence, I will give you a couple of my--my own definitions, what I like to

think about information. First of all, you can see it as negative entropy. So now I want

into the problem so I have to explain to you what is entropy. Entropy, in general, measures

the ignorance you have about the system. If your system has zero entropy, you know everything

about it. You have maximum information. If your entropy is large, there are certain things

you don't know about it and you have few information. And entropy is a well structured--established

concept and information theory. So how do you use it? You choose an alphabet. That could

be computational bases of two or one or anything else. Then in the next step, according to

that alphabet, you count probabilities. And once you have that probability distribution,

you can calculate the entropy of your choice. There's a whole family of it. Here, I've shown

you the [INDISTINCT] entropy which is widely used and very useful. But, I'm a physicist

and we can do the same in statistical physics. In that case, we choose our system of interest

and then we count the number of possible states which is denoted by capital omega, and then

we take the [INDISTINCT] of set number and KB as a constant--don't care too much about

the meaning. The massively interesting thing is that once all events are equally likely,

those two definitions of entropy actually coincide. This is one of the many links between

information theory and physics. So it sounds like combined science and then something different.

And in physics, we have the well-established second law of thermodynamics and that tells

you that in closed system, entropy does not decrease. So if we translate that argument

to information theory, we immediately know that in closed system, information cannot

increase spontaneously. That's very important to know. Next thing I would like to point

out that information is physical. Whenever you have a piece of information that comes

together with the physical carrier that can be the piece of paper you are writing now

at the moment, or it can be your hot wife on the computer. And for classical physics--for

classical information, we know from everyday life, I can change that information carrier.

I can write something on a piece of paper, I can scan it to my computer and I can print

it again. And if I didn't do obvious mistakes, I didn't lose any information. So that--that's

allowed by laws of classical physics, but as information comes along with the classical

carrier, the way I process information is bound to the laws of physics. So what happens

if I choose my physical carrier to be smaller and smaller until I reach the quantum limit?

Then the fascinating thing is the way I process information changes, according to the laws

of quantum mechanics. So what does that mean? So one thing is set, I cannot copy quantum

information, I can only copy classical information. And whereas classical information reliably

stores the information, in quantum mechanics, I always have to find decoherence. It's always

getting lost. So, coming back to the problem of DNA to use a long term storage, what I

just told you was those two points would actually mean that quantum mechanics is not any good

for DNA and if you really want to store your genetic information safely, you should keep

away from quantum mechanics. So what is the good point of it? Quantum mechanics allows

you to do more, and classical mechanics is a special case, and only has a certain set

of manipulations and quantum gives you more. So, now the question is, does nature exploit

this edge of being able to do more? Just a very short reminder of the notation, if you

have a classical bit, that's usually denoted by zero or one. If you have a quantum bit

or a QuBit, you put the zero and one in these brackets, as we call them [INDISTINCT]. And

I have one interesting feature, it sets a--sorry--that allows superposition. So in the classical

case, you have to decide whether the QuBit is zero or one. But in the quantum case, you

can combine it in a superposition. And then you have a mixture where the bit--the QuBit

is either zero or a one. You just don't know which one it is. So in superposition, it is

both simultaneously and in the mixture, you don't know which one it is. So I told you

that you cannot copy quantum information. The proof is this three-liner. So let us suppose

you could copy quantum information. Then you would have some--some unitary acting on your

way function-side so that actually copies an unknown state to your template. And then

I can suppose that that's [INDISTINCT]. It's a superposition of zero and one and I plug

it into the formula and I get that lengthy expression of the copied state, but the mathematical

formula of quantum mechanics also allows me to feed it in step by step. So I can feed

in first as Peter get one part which is copied to one one and then the alpha zero part which

is copied to alpha zero. That should be the same but we can see clearly it's not the same.

So assumption, is that we can copy quantum information was actually wrong and that's

causing the cloning theory. Actually, there was one special case where these two lines

are the same, namely Aiza, Alpha, beto or zero. And this tells you, which would roughly

correspond to classical information, so that's something you can copy. And another thing

I would like to mention in my introduction, is conditional entropy. So the conditional

entropy measures how much uncertainty, how much ignorance you have about a combined system

and observer and given that you have all of the observer's knowledge. And for anything

that we encounter in the real world, there's a fair assumptions that this conditional entropy

is bound to be low by zero. So the idea is that if my observer has a certain ignorance

about his own state, then the combined system and observer should have at least this uncertainty.

So but if we--if we are now dealing with this state, as was mentioned before this morning,

actually, I have full knowledge about the full system. I--globally, I don't have uncertainty,

but if I look at the state, the observer himself has, he actually has uncertainty. So this

quantity for quantum systems, this conditional entropy can actually be smaller than zero.

And whenever something like this happens, we call it entanglement. So whatever physical

meaning entanglement has, you can take it as very strange probability distributions

which allow you to--to achieve correlations which are classically not possible. So one

application, let's suppose you have a system which is in a mixture of zero and one. And

you would like to reset, it could be for example your memory, and you would like to reset that

to--to state zero. And what is usually called [INDISTINCT] state, is that a classical observer

has to pay one unit of work to extract or to erase that information. Is it any different

if we are dealing with the quantum observer? Yes. It could be that the quantum observer

actually has the other half of a maximally entangled state and then the system has the

same correlations. As was shown recently, in that case, you can actually extract one

unit of work and you erase information to reset it to zero. And now, we are talking

about biology. Whatever small enzymes, molecules and other systems are wiggling around in your

biological systems, it could be that it's small enough to be a quantum observer. And

then suddenly, the whole set up changes. Instead of needing to pay work, you can actually extract

work and you can do the same. So it might be that for those small biological systems,

we need to change the way we think about it. And another thing I would like to mentions

is, information is a subject of quantity. It depends on the knowledge you can have.

And that might be different for different observers. So, this was the introductions.

It was a lot of concepts. That's the only slide I will mention about decoherence. You

can talk a lot about it, but I will abbreviate it to the time a system can maintain its quantum

coherence. It's roughly inverse proportional to the mass and the temperature. So why don't

we see any quantum effect on the real life? We are massive. We have a lot of mass, and

the second reason is we are hot. We are at 300 Kelvin, that's a lot of temperature. So,

whenever you have these two effects, you would believe that you don't have quantum effects.

So finally, information in DNA. So, probably most of you already know this molecule. Let

me just give you a brief reminder. So, this DNA is this really single long molecule. And

outside here, you have some phosphate that bound into sugar stabilizing, so DNA. But

it's actually--those four nuclide acids that contains a genetic information. And when I

first looked at it, it's those molecules, I thought, "Well, they are pretty small compared

to our computers, what we encode in a bit in a computer." And because here we are--we

have four different bases, each molecule encodes two bits. Yes, and then these two bits are

arranged in a linear, away into the two--two ends have opposite information. Now, the interesting

question is, how do you actually access that information? It's not enough to store with;

you actually have to be able to read it out. How do you do that with these small systems?

So, let's look at only one of them, cytosine for example. So, that's for you on the right

side, isn't it? No, that's for you on the left side. So on the left side, it's actually

bound to the phosphate backbone, so you cannot access it. Up and down of this cytosine here,

you have electron clouds and other nuclide acids, so you cannot access that part either.

So, the only part where you can actually access that molecules is on the right side. So--and

this is actually what's used in biology. Here we have those atoms, that's Nitrogen and Oxygen;

and single protons can bind to it. So now, the idea is to use acquisition of those protons

to encode the identity of that molecule. Another thing I should mention is, that this aromatic

ring you see there, that's actually--even though I consider it small, for quantum mechanics,

it's actually quite large. So this is something we can safely assume to be classical information.

Whereas the position of a single proton, a single proton is due to loss of quantum mechanics,

that might tunnel. So, this leads me to this notation that's a little bit sloppy but it's

good for transferring ideas. So, the classical information that we are dealing with--since

the molecule cytosine is something I would encode in this quantum state which means that

the lower two slots where the proton could be empty, and the upper slot is filled; so

that's denoted by those zeros and ones. So, then how do you--how do you combine it? Cytosine

always pairs with Guanine and so Guanine has the opposite slot, so the lower two slots

are filled and the third one is empty. And then, when you bring those two molecules together,

you can form H bonds. And you can only have one proton in these H bonds; so that's why

it's necessary to have this sort of matching proton distribution. So here, it's really

a lock-and-key mechanism. Same holds for Thymine and Adenine. So, does this mechanism work

perfectly? No. What can happen is that here your cytosine goes into its rare form, which

means that its proton tunneled to the second slot; that's allowed you to do quantum mechanics.

But then, when we go to the look-up table of the encoding, so it actually looks the

same like a Thymine. And as a consequence, because the quantum information pretends that

this molecule is a Thymine, the Adenine thinks that it can bind to it; and that's one way

of how you can get mutations to your system. So, once again, you have here a classical

bit which you encode in this quantum information, and epsilon is some sort of a tunnel probability.

So, epsilon is small. So most likely, it stayed in this state, you encoded it. But there was

a small probability that your quantum information was--test-wide into a different state. So,

this is quantum information into transversal direction. So, let's make a little jump to

the longitudinal direction. All these--these nuclide acids, they are more less plan a molecules

being surrounded by electron clouds. These electron clouds, because you're dealing with

aromatic rings, are highly delocalized; so that's why I draw them in such a sandwich

notation. So now, what happens is that these electron clouds carry negative charge. And

we know that adjacent negative electron clouds will repel each other. The intriguing thing

is that this actually leads to correlated excitations lowering the ground state energies.

So, different charged clouds kick each other, and then they redistribute their charged distributions;

and that can actually lower the ground state energy. Now, that effect is called Van der

Waals interaction or Van der Waals forces. And you actually need the coherence between

neighboring sites to get the attractive part of the force. But now, this is also has nontrivial

implications. So, first of all, neighboring sites are entangled due to these continuous

interactions. And also, the electron cloud of one site carries information about the

identity of the other site. So, if I'm a Thymine here, and I'm adjacent to an Adenine, this

Adenine influences my own electronic state. If there would be a cytosine next to me, my

own state would look different; and that's substantially different from classical computing.

So, my own identity is influenced by the neighbors I have in the DNA chain. Now, I just gave

you two examples where you can expect quantum information to be present in DNA. And maybe

the one or other just was irritated because we are room temperature-systems. So, how does

it work together that I told you, if you have massive hot systems at room temperature, you

cannot have entanglement. Well, I didn't tell you everything, details matter. So, you can

analyze a very generic model of couple thermal oscillators. And then you actually see that

the absolute temperature does not matter. It's a temperature, so kBT, the thermal energy

compared to the interaction energy that matters. And if that coefficient is small, then you

can expect quantum effects to be present. And if you pluck in all the numbers we have

for this longitudinal entanglement, you see that thermal energy is actually very small

compared to the interaction energy. So DNA has optical frequencies; and this means that

the thermal noise cannot excite those optical frequencies. So, this quantum information

we are talking about is basically in its ground state, even at 300 Kelvin. So, here was a

screenshot from a computer program where you do something with DNA; you've seen it many

times before. And to sum it all up, what I told you at the previous slides, everything

that you can see on this picture is classical information. The black stuff and the double

helix that you cannot see, that's a quantum information. So, they--I haven't discovered

any good way how to--how to picture correlations. Probably, there was no way; so that's why

nobody ever draws quantum information. But the next time you see such a double helix,

you know, okay, all the stuff I do not see, that's a quantum information. So basically,

what happens is this classical information by which is usually drawn here is embedded,

is sandwiched into quantum information. And most likely, this classical information is

never accessed; you can only--because it's inside--all the quantum information, you can

only access the quantum information or the electron clouds and the protons. So mathematically,

you can describe that as a quantum-classical state. So, let's suppose that X is a string

of classical symbols; you would denote that the state has two components. So the first

one denotes the classical information, this is diagonal and its basis has no coherence.

But this actually comes along with some sort of quantum information. And so, X for example,

could be the string of your DNA; and then it is embedded in this cloud of quantum information.

And Paul Davies called this sort of quantum information, shadow information. Because in

this quantum information, you have at least one copy of the information in your DNA, if

not, more copies. And if you want to decode your classical information, you measure the

quantum part. But it can happen that the quantum part of science is not fully distinguishable,

and this gives possibility for mistakes. So, coming to the most important question, does

it matter at all? Well, I do not know for certain; but I think there are many things

quantum allows you to do. And if quantum gives you an advantage, this four billion IT project

probably discovered how to use it. Let me come back to the channel picture I introduced

in the beginning. So, you would like to send some classical information from the sender

to the receiver. We do it everyday. We send text messages, we send email, we talk; that's

also classical information which uses classical channels. The only problem is that this probably

doesn't take place in DNA; because the system you are talking about is too small to really

have a full classical channel. So it's more likely that you're dealing with a quantum

channel. You can send classical information in the quantum channel, that's no problem.

So you encode your classical information on your quantum system, you send your quantum

system, then you make a measurement on it and decode the information it carries. And

there are two channels I would like to compare: The normal quantum channel, and the entanglement

assisted quantum channel, where actually the sender and receiver initially share entanglement.

And then, I will talk about the capacity of channels. And this roughly measures how much

information can be transmitted in this channel. So that's a number between zero and one. If

it's one, you can fully transmit all the information you send in. And if it's zero, your channel

is useless and you cannot send any information. Calculating channel capacities is very, very

difficult; and those capacities are not known. But for some simple channels, they are known,

and one of them is called Qubit depolarizing channel. So, what happens here, you take your

way function, sign of X, and you send it to the channel. But it can actually happen, that

in this channel, it suffers from some sort of noise; as we can expect it with biological

systems. And then, with probability one minus epsilon, this channel gives you the original

way function; and with probability epsilon, it sends you something completely random.

So that's the Qubit depolarizing channel. And now, if you would like to encode your

classical information X, so X could be added into mean or whatever. You encode that in

a certain way function, you send it through your noisy channel, and with some probability,

you recover X. But in some cases, you guess incorrectly and you recover Y. So, how often

you guessed correctly and how often you guessed incorrectly, is characterized by this channel

capacity K1. And now, you can--you can use the same channel. The only difference is that

now, sender and receiver initially share maximally entangled states and so you have capacity

KE; E for entanglement. And the beautiful thing is if you use entanglement, you can

double your channel capacity. So, we have a system where you would like to transmit

classical information. It is reasonable to assume that you can create this entanglement

resources and this entanglement would allow you to double the capacity of your noisy channel.

So that's something we're thinking about. Something completely different, how you might

use entanglement in DNA is for communication along the chain. When I read up on the literature

on how little motors go along the DNA and achieve things, I always wonder what—how

does it work? How do these motors actually know what they are supposed to do? So let

us suppose that each of these balls represents a site in your DNA and what I do is I wiggle

the one end of it and then you can calculate what's happened to it. Actually, after some

time, you will get entanglement between the first side where you shake your end and the

nth side could be the 10's or 20's or 30's side along the chain. And suddenly, these

two far apart side share entanglement, and entanglement means it's a half correlation.

So the question is, can you use those correlations for communicating along this one dimensional

chain? And the next thing is something where my own ignorance comes up. I do not know too

much about protein folding but I have a background in Information Science so I would like to

ask a question to people who know more about Biology. So when I would like to fold a protein,

I start with my DNA, which is a one-dimensional sequence of information. So, in order to fully

describe my--the classical information in DNA, I only need to know this one-dimensional

sequence. Then I make a copy to RNA and the information content did not change. In the

next step, I translate pairs of [INDISTINCT] of my RNA into an amino acid. Now, there's

some sort of quote and quote, you might argue that you lost some information—-I'll ignore

that effect for the moment. And then it's a four step, this is one-dimensional chain

of amino acid, actually folds into a three-dimensional structure. So let's look at it again. You

start with DNA, messenger RNA and this chain of amino acids and because they are all linear

arrangements, I would argue that roughly up to small errors that can carry the same amount

of classical information. And then you fold a protein, and it's getting a three-dimensional

structure, and the shape is vital to its functioning. But now, you need to store more information.

In addition to the sequence, you have the position information and in my opinion, that's

actually an increase of information. But we also know from the second law that in closed

systems, information cannot increase spontaneously. Now I know that creating a protein is far

away from being a closed system but my question to the biologists is actually, "Where does

this additional information come from?" If you think about it in detail, that's actually

not that trivial. Does it come from the time sequence in which you assemble the protein?

Does it come from some sort of laws of quantum mechanics? Do you have some sort of quantum

information actually also taking place? If anybody can tell me, I'll be very happy. So,

[INDISTINCT] question that's actually taking from a German piece of literature, let's go

to Faust, it's a very nice book; I can only recommend reading it. And so it's sort of

an important question. So the important question is, does quantum information matter? And there's

one way to test it. So you take two identical strings of classical information and by some

means and one string, you change the quantum information. There are some ways to disturb

quantum information. And then you actually look—-does it fold in the same configuration

or does it fold differently? If two strings with the same amount of classical information,

but different quantum information fold into different chains—-into different configurations,

different shapes, that would actually be a good argument that quantum information matters.

And does this—-is this line of thought generalizes to other situations. When you wonder, does

quantum matter? Well, disturb it, shake it, destroy it, and see if it makes a change and

then you'll know if quantum matters. So, last point, comparing those different platforms

which all have to do with information flow. If I have a classical computer, I would initialize

it and either zero or one or any other computational basis. When the--for DNA, I argue that you

use quantum classical states and for quantum computing, I didn't talk too much about quantum

computing, so if you are unfamiliar with the subject, you can just ignore those in the

last column. You have whatever space your quantum computing is assigned to with its

Hilbert space. Then you let those bits attach and for classical computers, that should be

fairly independent. If I store a value of zero here, this is independent if next to

it is a zero or a one. For DNA, the value—-the quantum information of a single side strongly

depends on the quantum information on the next side. And for quantum computing entanglement,

it seems to be the crucial quantity, so then you fully exploit it as a non-local correlations.

With classical computation, you do gates like 'and', 'or', 'not' and many more. In quantum

computing, you have a universal set of unitary dates and I have to say that in DNA, I have

no idea what sort of gates are possible. That would also be interesting if--to work together

with someone in biology to actually classify the allowed operations on DNA. When it comes

to cutting DNA and reassembling, that's getting pretty loud. And also, non-equilibrium will

be the most interesting case. What I said about shaking one end and seeing how the correlation

spread along the chain, that's non-equilibrium. The gate time will be short for classical

and quantum computing. In classical computing, the shorter the date—-gate time, the faster

your processor works. For quantum computing, you always need to find the decoherence, so

that's why you have to make it short. DNA will be a bit—-a little bit different, because

you have this sort of continuous interaction. And then finally, the way out for a classical

computer that's purely deterministic and you make only a few errors. With quantum computing,

it's actually statistical. You need to repeat the same experiment many times before you

can actually have a read-out and DNA is again somewhere in the middle. So if you want to

read-out DNA information, you have a single shot, you have one try to do it. So given

all the quantum that's involved, I would actually like to know the accuracy of that read-out.

So, there's many, many more things you could compare but what you see already is that DNA

seems to sit somewhere in the middle between classical and quantum computing. So the conclusion

of this talk is that both classical and quantum information should be considered for full

understanding of DNA, even if DNA is probably not a full quantum computer. And there are

many people I would like to thank for, for help for discussions, for preparing this talk.

So, Mile Gu, Oscar Dahlsten, Kavan Modi, Giovanni Vacanti, Janet Anders, my supervisor Vlatko

Vedral and there are probably many more. And yeah, thank you for your attention.

>> I'll have the mic then. I have three questions, actually comments. The first is, I would like

to solve your problem. Actually, there's no information gained.

>> Yeah. >> Because you have to look at the entire

environment which includes water and this is a typical problem in protein folding. When

you include water, it's an entropic force, so you calculate all the energy and you minimize

your energy of the entire system, which is DNA with water or protein or peptize with

water, and you end up with equilibrium confirmation, which is the folded state, and that corresponds

to the minimum energy or maximum entropy. So, I mean, of course, we have to do detailed

calculations but I maintain that when you do that, you will end up with possibly a loss

of information, not gain of information. >> Of course, when you consider the whole

box, then of course, you cannot gain information, but still, I would like to understand how

this information from the water molecules actually...

>> No, it's very simple because water molecules attach to peptizer, I mean, acids and by doing

so, they lose information about their conformational freedom of movement. So free water molecule

has rotation degrees in transitional, when it's bound, it loses this freedom and that's—-it

can be quickly calculated entropy gain or information loss. The idea of the superposition

of quantum and classical wave function for the DNA, I think is a great one. And I think

you call this shadow information or something, but actually it can be made very concrete.

We think about DNA as the sequence of nucleotides, you know, the code. But actually, it's not

letters; these are molecules, they are vibrating. So the vibrating—vibrations around the bonds

are like wave functions. So this is really quantum-mechanical oscillations and that can

be your shadow, if you will. Because if you think about just the sequence, yes. And these

vibrations actually reflect the neighborhood. So what you talked about, the importance of

neighborhood, it's preserved by the nature of the vibrations. And finally, very quick,

the gates and the read-out, I think there's a whole slew of proteins like conscription

factors and DNA polymer razors--enzymes that participate in this and these are the readers

and the writers and the gates in all this. Anyway, that's all I have to say.

>> So, Eddie had mentioned [INDISTINCT] but [INDISTINCT].

>> Could you get up and speak louder? >> Yeah, okay. So, did you mention at all

why the quantum coherence could survive at room temperature for these DNA molecules?

>> Yes. So one pound of the quantum information is encoded in this electronic degree of freedom

and it just happened that you have optical frequencies for this system and your room

temperature cannot excite those optical frequencies, so that's why you are basically on the ground

state. Another thing is that you have this double helix and that's actually shields very

well and any noise from it. >> So you are saying this is-—this has nothing

to do with a non-equilibrium state of this DNA vibrational mode? So you are saying even

in a static form? >> Yes. So far, my calculations are only static

and the next step I will look at, at non-equilibrium. But even in static, you have a massively stable

system—-massively stable in the sense of maintaining quantum information because of

those optical frequencies. >> [INDISTINCT]

>> Well, with the proton tunneling, it's more delicate because you can only measure on one

basis and then it's actually undistinguishable whether you have a coherent superposition

or a mixture. But for tunneling to take place at some point, it needed to be a superposition,

that's why I denoted [INDISTINCT]. >> [INDISTINCT]

>> Unfortunately, I'm a physicist. I hope that some biologists in the audience can answer.

>> Yeah, because it is—-it goes to the comparison at the end that you did a table that you compare—-yeah,

classical computing DNA and quantum computing. I mean, I don't see any discussions of the

coherence [INDISTINCT] skills here. So I think... >> We can add it in the next coffee break.

>> Okay. >> Let us take one more question then we will

have a break. >> I think it's—-I mean there are lots of

experiments we know about that we show entanglement over space. Now, I wonder if you're suggesting

that there's entanglement over time with DNA sort of being the string between.

>> That's a slight misunderstanding from the notation I used. You can have entanglement

over time. Here, I do not propose it. It's that you have the classical information in

the past which you want to send into the future and each step might use quantum mechanics,

but that's a different problem. >> Okay, I'd like to thank our speaker one

more time please.