Undergrad Help! I Don't Understand Quantum Darwinism

[Paul Parnell]

TL;DR

Can someone explain what a pointer state is?

I have been trying to understand quantum Darwinism and I just don't get it. It seems to be like decoherence yet I don't see any value added. I don't think I'm even understanding it. I cannot even understand what a pointer state is supose to be.

Apologies if this is the wrong place to ask but I don't see the Quantum Foundations and Interpretations forum. I really don't want to discuss the merits of any interpritation. I just want to understand the claims.

 

[PeterDonis]

Moderator's Note: Thread moved to quantum foundations and interpretations forum.

I really don't want to discuss the merits of any interpritation. I just want to understand the claims.

Quantum Darwinism is an interpretation, so discussion of it belongs in the interpretations forum. As you will see from the forum guidelines, this forum is not for discussing whether interpretations are "right" or "wrong", but for discussing what they say.

 

[Paul Parnell]

Thanks. I did read the guidlines but as I said I could not find the Quantum Foundations and Interpretations forum. And now it appears as if by magic. Were you hidiing it or am I really that blind?

 

[PeterDonis]

I could not find the Quantum Foundations and Interpretations forum. And now it appears as if by magic.

It is a little confusing since it's a sub-forum of the Quantum Physics forum, so it doesn't appear on the PF front page. From the front page, you have to go to the Quantum Physics forum, and then there is a link to the Quantum Interpretations and Foundations forum at the top of that page. Or, now that I've moved your thread there, you can click the link at the top of your thread.

 

[Lord Jestocost]

Summary:: Can someone explain what a pointer state is?

I cannot even understand what a pointer state is supose to be.

I think it means the following:

"If the instrument interacts with a quantum system which is already present in one of measurement eigenstates ($|\psi_+\rangle$ say), then the total system (quantum system + instrument) must evolve into product quantum state $|\psi_+\rangle|\varphi_+\rangle$, i.e.,
$$\hat U|\psi_+\rangle|\varphi_0\rangle=|\psi_+\rangle|\varphi_+\rangle$$
or, in other words, if the quantum system is in a state (with probability = $1$) corresponding to a definite pointer position, then the measuring device state must evolve into a state where the pointer is pointing to the proper place. This is what happens in the laboratory.
Similarly, we must have
$$\hat U|\psi_-\rangle|\varphi_0\rangle=|\psi_-\rangle|\varphi_-\rangle$$
Using these special case results, we then have for the evolution of any arbitrary state the result
$$|\Phi\rangle=\frac 1 {\sqrt 2}(|\psi_+\rangle|\varphi_+\rangle+|\psi_-\rangle|\varphi_-\rangle)$$
where the measuring device states $|\varphi_+\rangle$ and $|\varphi_-\rangle$ correspond to the pointer ending up at $+$ or $-$, respectively.
This result suggests that the measuring instrument evolves into superposition state in which pointer has equal probability to point either to the left or right, but not into a definite pointer state…..
….This state will remain a superposition (pointer does not point) unless we allow for collapse so that the pointer can point (take on a definite value)!"

From: Quantum Theory in Search of Reality by John R. Boccio (pp. 347 – 348)
http://www.johnboccio.com/TQM/index.html

 

[Paul Parnell]

Ok, that's as clear as mud. But wading through it it is just a statement of the measurement problem and the pointer state is just wave collapse. But the text also points out that there seems to be no way to get to a pointer state. The measuring device must be seen as being in superposition. Anyone looking at the device must be in superposition anyone they talk to as well. Wigner's friend. The measurement problem. Standard stuff.
But in the context of quantum Darwinism what are we talking about here? How can the pointer state cause unitary collapse? What is it that it can do this? I just don't see anything being copied or any Darwinism going on.

 

[Lord Jestocost]

Maybe, the following might be of help (I think - without guarantee - that Quantum Darwinism tries to solve the problem of outcomes):

"From our discussion in Sect. 2.2.1 we know that such a superposition is fundamentally different from a classical ensemble of states, i.e., from a situation in which the system–apparatus combination actually is in only one of the component states $|s_i\rangle|a_i\rangle$ but we simply do not know in which (see also the analysis in Sect. 2.4.2 above). Therefore, unless we supply some additional physical process (say, some collapse mechanism) or provide a suitable interpretation of such a superposition, it is not clear how to account, given the final composite state, for the definite pointer positions that are observed as the result of an actual measurement.

This problem can be further broken down into two distinct aspects. First, we are faced with the question of why we do not perceive the pointer of the apparatus in a superposition of different pointer positions $|a_i\rangle$ at the conclusion of the measurement (whatever it would actually mean to observe such a superposition), i.e., why measurements seem to have outcomes at all. And second, we may ask what “selects” a specific outcome. That is, why do we observe, in each run of the experiment that realizes the measurement, a particular pointer position $i$ (and thus a particular pointer state $\mathbf {|a_i\rangle}$), as opposed to one of the other possible states $|a_{j \neq i}\rangle$? We shall refer to both issues jointly as the problem of outcomes." [Italics in original, bold by LJ]

From: DECOHERENCE AND THE QUANTUM-TO-CLASSICAL TRANSITION by Maximilian Schlosshauer (Corrected Third Printing, chapter 2.5.4 "The Problem of Outcomes")

 

[Paul Parnell]

Well yes but I don't see how the quoted text addresses the problem.

1) Why we do not perceive the pointer of the apparatus in a superposition... Quantum mechanics is about the distribution of quantum information. The shape of the quantum probability distribution is a reflection of the quantum information we contain in principle. Interacting with a quantum system will change that radically. so "seeing a superposition" is an oxymoron. Deciding what that means physically is a little more complex but I think simple decoherence does it well.

2)Why do we observe, in each run of the experiment that realizes the measurement, a particular pointer position... I don't see that this question has an answer or even needs an answer. But specifically I don't see how quantum Darwinism answers this question.

Imagine a single quantum particle that is in a superposition of two states. How would measuring that state tell us if the particle was in quantum superposition or just a classical particle in some random state? It couldn't.

Now imagine two particles where they have interacted and so are entangled. Now we can define correlated probabilities that violate Bell's inequality. Classical systems cannot do this so this is a sign of quantum coherence.

Now imagine three particles. If you look at any two particles you still may be able to see violations of Bell's inequality but it will be more fuzzy because of interactions with the third particle. It contains some of the quantum information. But by observing all three particles you can still sharpen the Bell violations. This is the beginning of decoherence.

As you add more and more particles the Bell violations of two particles get fuzzier and fuzzier. This looks like wave collapse but that is an illusion. As long as you keep track of all of the particles you can in principle reconstruct the Bell violations.

Now imagine a huge number of particles in the form of a cat. We put the cat in a box with the Schrödinger apparatus. As the contents of the box evolves it becomes a superposition of all the possible ways the contents of the box could interact. Because there are a huge number of particles the alive/dead state of the cat looks very classical. But this is an illusion. The cat must still be considered to be in a superposition of alive/dead.

Now imagine a large quantum computer running a very large complex program. If the computer had about 10^30 memory elements you could program in a cat accurate down to the molecular level. As the program runs it becomes a vast complex network of entangled states. Because there are a huge number of memory elements the macro alive/dead state of program cat looks very classical. But this is an illusion. Each individual memory element is in a superposition of states and entangled with other memory elements. The wave function has not collapsed it has only become vastly convoluted.

If there were some unitary process to cause Schrödinger's cat to collapse into a particular alive/dead state then it should also happen to program cat. If it happens to program cat then the quantum computer would decohere and so crash. That's not what quantum mechanics predicts.

So this unitary collapse process seems problematic for quantum mechanics. I don't understand how the unitary process is derived. In particular I don't see anything that looks Darwinian. I wonder if the whole thing is motivated by a need for an objective collapse mechanism. I don't think that will work. While we may be forced to see the cat as being in a superposition of states I think the cat knows very well if it is breathing poison. This seems incompatable. Welcome to quantum mechanics.

 

[PeterDonis]

this unitary collapse process

There can't be any unitary collapse process. The state transition involved in collapse, if we suppose it to be an actual process, is not unitary.

 

[Paul Parnell]

I agree but am I correct in my understanding that quantum Darwinists are trying to develope such a unitary collapse process? Or at least that quantum Darwinism implies such a thing?

What do you think of decoherence as an explanation of the quantum/classical divide?

 

[PeterDonis]

am I correct in my understanding that quantum Darwinists are trying to develope such a unitary collapse process?

So far nobody has given any actual references that explain what quantum Darwinism is. We have no way of addressing this question here unless we have some specific references to look at.

 

[Paul Parnell]

So far nobody has given any actual references that explain what quantum Darwinism is. We have no way of addressing this question here unless we have some specific references to look at.

All I can give you is pop-sci articles. For example:

https://physicsworld.com/a/quantum-darwinism-spotted-in-diamond-spins/

https://www.quantamagazine.org/quan...bjective-reality-passes-first-tests-20190722/

I came here because it just seems like nonsense to me. Not being a physicist I seek guidence.

For example pointer states do not "copy" themselves into the environment. They entangle themselves into the environment. Thus what is generated is not vast numbers of pointer states that outcompete superposed states. What is generated is a vast network of entanglements and superpositioned states. It looks "classical" because the phase relationships are effectively randomized making it effectively impossible to see coherent quantum phenomena like Bell violations or interference patterns. If you could trace down all the environment particles that carryied away part of the quantum information you could reconstruct the coherent quantum phenomena.

Quantum Darwinism isn't just wrong. It is unnecessary. Decoherence does not need it.

 

[PeterDonis]

All I can give you is pop-sci articles.

Those are not valid sources for PF discussion. If you cannot find any actual textbooks or peer-reviewed papers, there is nothing to discuss.

I suggest that you chase down some links in those pop science articles, or look up some of Zurek's papers on arxiv.org, and start a new thread based on a valid reference if you find one.

Quantum Darwinism isn't just wrong. It is unnecessary. Decoherence does not need it.

Basing an opinion on pop science articles is not a good strategy. Nor is there any point in trying to discuss or refute such an opinion, since none of us have any idea whether the understanding of quantum darwinism the opinion is based on is correct.

 

[PeterDonis]

Thread closed due to lack of any valid reference on which to base discussion.