What does decoherence have to do with phases?

[Talisman]

Again, you're not addressing the issue I'm raising. You can't know that the two-qubit system is in this state unless you prepared it that way. If the second qubit is a random photon that happened to pass through your experiment, you didn't prepare the two-qubit state, so you don't know what it is.

I realize Aaronson does not explicitly state in his article what I just stated above. That doesn't mean he disagrees with it. He just didn't say it. What I say is obvious. If you don't agree with what I say, then give me an actual argument. Don't just keep repeating what Aaronson says. I know what's in Aaronson's article. I also know that what's in Aaronson's article does not address the issue I'm raising.

I'm afraid we keep talking past each other, and I don't know how to resolve it. I will try one more time, but I am afraid I have reached the limit of my ability to communicate here.

Yes, I agree that you can't know the state of a random photon passing through your lab. And yet it is also the case that if you do prepare the two-qubit state as given, and measure only the first particle (and hurl the other off into space so that you can't measure it, or even simply decide to not measure it), the statistics of that first qubit for all observables will be identical to those of a qubit with definite relative phase whose phase information has been lost (or equivalently, averaged over all possible phases). "Decoherence" is a subjective interpretation given to the condition where it becomes "hopeless" to recover that particle (and whichever others got entangled), whatever "hopeless" means. Most of us would indeed consider trillions of air molecules and photons "hopeless" to carefully measure, but even a single one zipping off to Andromeda qualifies.

 

[Talisman]

Or, as Demystifier says here: https://www.physicsforums.com/threads/irreversibility-vs-reversibility.909761/

Yes, like the ocean, [decoherence is] reversible in principle but irreversible in practice.

When it becomes "irreversible in practice" depends on the technology available to you.

 

[PeterDonis]

I agree that you can't know the state of a random photon passing through your lab.

Not just the state of the photon, but the joint state of the photon and the qubit in your lab, if the photon becomes entangled with the qubit by some random interaction.

if you do prepare the two-qubit state as given

Then obviously your first qubit can't be entangled with some random photon that passed through your lab, because you prepared your first qubit to be maximally entangled with a second qubit that you control. So this is simply a different scenario from the one I have been talking about.

The reason I have been emphasizing this difference it that it explains why there is no decoherence in a Bell inequality experiment without having to make highly implausible claims about how whether or not decoherence is produced by entanglement depends on whether or not we measure the second particle afterwards. Instead, we have the much easier claim that whether or not decoherence is produced by entanglement depends on whether or not the entanglement is produced by a controlled preparation process or a random, uncontrolled interaction.

To put it as succinctly as possible: instead of saying "entanglement destroys coherence", I would say "uncontrolled entanglement destroys coherence". And I think the latter statement better reflects the overall theory of decoherence in the literature.

 

[PeterDonis]

When it becomes "irreversible in practice"...

Is a different question from the question of under what conditions it is produced by entanglement.

 

[PeterDonis]

"Decoherence" is a subjective interpretation given to the condition where it becomes "hopeless" to recover that particle

If we adopt my statement of when entanglement destroys coherence, we have an easy answer to this one too: it becomes "hopeless" when the other particle, that we let fly out of our lab instead of measuring it, undergoes entanglement with other particles in the environment due to random, uncontrolled interactions. The decoherence in this scenario doesn't occur until that happens; it doesn't occur at the initial entanglement during the preparation process because that process was a controlled preparation. So we don't have to say that whether or not the entanglement during the preparation destroys coherence depends on what we choose to do afterwards. It doesn't; the entanglement during the controlled preparation never destroys coherence. Only further random interactions of the second particle, which will only happen if we choose not to measure it, do.

 

[Talisman]

To put it as succinctly as possible: instead of saying "entanglement destroys coherence", I would say "uncontrolled entanglement destroys coherence". And I think the latter statement better reflects the overall theory of decoherence in the literature.

I am prepared to accept that "decoherence" is more commonly used in the literature for uncontrolled entanglement because (1) the environment state is generally unknown and (2) what's the point of preparing a known entangled state if you're just going to ignore one of the partners?

At the same time, I have shown explicitly (and provided references for) how preparing a controlled (strong) entanglement has the effect of making the single-particle statistics of each individual particle identical to those of one whose phase has become unknown -- i.e., one that has become incoherent. (It was also shown in those references, though not discussed here, how the two-particle statistics will still show "interference" by virtue of the joint system still being in a pure state). This has become a common (if toy) example of "decoherence" in the quantum computing community, so please take that as you will.

Thanks again!

 

[Talisman]

This has become a common (if toy) example of "decoherence" in the quantum computing community, so please take that as you will.

And on that note, here is what Nielsen & Chuang (the bible of QC -- at least when I was in school) have to say about the confusion:

An unfortunate confusion of terms has arisen with the word ‘decoherence’. Historically, it has been used to refer just to a phase damping process, particularly by Zurek[Zur91]. Zurek and other researchers recognized that phase damping has a unique role in the transition from quantum to classical physics; for certain environmental couplings, it occurs on a time scale which is much faster than any amplitude damping process, and can therefore be much more important in determining the loss of quantum coherence. The major point of these studies has been this emergence of classicality due to environmental interactions. However, by and large, the usage of decoherence in quantum computation and quantum information is to refer to any noise process in quantum processing. In this book, we prefer the more generic term ‘quantum noise’ and tend towards its usage, although occasionally decoherence finds a proper place in the context.

 

[PeterDonis]

This has become a common (if toy) example of "decoherence" in the quantum computing community

I would describe this as the QC community hijacking the term "decoherence" and changing its meaning from the one that had been previously used in the literature. You quote Nielsen & Chuang as saying there is "confusion" about the usage of the word. That seems a bit rich since Zurek, whom they refer to, basically invented the usage of the word they are saying there is confusion about. N&C even describe Zurek's usage (which is basically the one I have been describing) in the quote you give, so they clearly understand it. They just think it's fine to hijack the term.

At the very least, it seems to me that it would have been better for the QC community to invent its own term instead of hijacking one already in use. Like, oh, I don't know, "quantum noise", which N&C actually use in the quote you give, but it never seems to occur to them that they could use that term instead of the term "decoherence" instead of claiming that everybody else in the QM community was using the term "decoherence" wrong until they came along.

 

[PeterDonis]

I would describe this as the QC community hijacking the term "decoherence" and changing its meaning from the one that had been previously used in the literature.

And to tie this back to the original question of this thread: as the QC community uses the term "decoherence", it does not appear to me to have anything to do with phases. But as the rest of QM uses the term, i.e., according to the meaning it had before the QC community hijacked it and changed its meaning, it of course does have to do with phases--N&C themselves describe how, and their description matches what has been said earlier in this thread.

So this whole discussion has had nothing to do with actual physics; we all agree on all of the actual physics involved. The only issue has been what actual physics the term "decoherence" refers to. That's a matter of words, not physics.

 

[Talisman]

You quote Nielsen & Chuang as saying that Zurek was confused about the usage of the word.
...
claiming that everybody else in the QM community was using the term "decoherence" wrong until they came along.

I honestly don't know how you took all this from the N&C quote. They simply say that there exists unfortunate confusion, which they even seem to be trying to correct by avoiding the term where possible.

it never seems to occur to them that they could use that term instead of the term "decoherence"

I would describe this as "seeming to occur to them":

In this book, we prefer the more generic term ‘quantum noise’ and tend towards its usage

But I am happy to agree to disagree on interpretation here, too.

 

[Talisman]

Anyway, all's well that ends well. They have a complete section on phase and amplitude damping, and those will probably help me understand those effects from the QC perspective, which is the one I understand best.

Thanks again, and sorry for the confusion!

 

[PeterDonis]

I honestly don't know how you took all this from the N&C quote. They simply say that there exists unfortunate confusion,

"Unfortunate" is an opinion. Why do they have that opinion? Because the meaning they would like the term to have is not the meaning it actually had in the literature before they came along.

which they even seem to be trying to correct by avoiding the term where possible.

Avoiding the term and using other terms like "quantum noise" would be fine. But in this thread you don't seem to be adopting that policy. You seem to be adopting the policy of using the term to mean what you want it to mean, not what it meant in the literature before the QC community hijacked it.

 

[PeterDonis]

They have a complete section on phase and amplitude damping

Yes, and so does much of the decoherence literature outside the QC community. As I said, we all agree on the actual physics, which is good.

 

[f95toli]

I would describe this as the QC community hijacking the term "decoherence" and changing its meaning from the one that had been previously used in the literature.

This would be true if it was correct. Note however that N&C is quite an old book. These days, when we in the QC community talk about decoherence we most definitely mean loss of phase due to e.g. external noise.

See e.g. section III in the following review
https://arxiv.org/abs/1904.06560

That is, we've mostly adopted the language of say ESR and NMI (which is hardly surprising since e.g. spin qubits is experimentally essentially just ESR in the "quantum regime")

For the record, I've worked on QC related tropics for the past 15 years or so. One of the topics my team works on is understanding decoherence in superconducting qubits ; I don't claim to be an expert on the theory (I am an experimentalist) but I am very familiar with how the term is used. Again, in what I would call mainstream physics "decoherence" has little to do with how Zurek and others used the term back in the day where focus was more on foundations; these days reducing decoherence often boils down to proper engineering (using the right materials, low-loss dielectrics, making sure that you are not Purcell limited etc). The physics is very well understood.

 

[PeterDonis]

N&C is quite an old book

The original edition, as far as I can find out, was in 2000. The term "decoherence" in the literature with the usage I described goes back, AFAIK, to 1970 in a paper by Zeh. IIRC Zurek's first comprehensive review was published in the early 1980s.

 

[PeterDonis]

The original edition, as far as I can find out, was in 2000. The term "decoherence" in the literature with the usage I described goes back, AFAIK, to 1970 in a paper by Zeh. IIRC Zurek's first comprehensive review was published in the early 1980s.

This review by Schlosshauer gives an excellent list of references:

https://arxiv.org/abs/quant-ph/0312059

 

[PeterDonis]

the following review
https://arxiv.org/abs/1904.06560

The references in this paper give the 10th Anniversary Edition of Nielsen & Chuang as being published in 2011, which would mean the original edition was published in 2001.

 

[PeterDonis]

what I would call mainstream physics

If by this you mean "quantum computing", I would agree that the usage of "decoherence" is not necessarily the same as the usage of Zurek et al.. But I don't think "mainstream physics" is limited to QC, and I don't think the term "decoherence" is used outside the QC community in the same way that the QC community uses it.

If there is a paper by someone in the QC community that gives a detailed argument for why the QC usage of "decoherence" makes more sense than the previous usage, I would be interested in reading it.

 

[PeterDonis]

loss of phase due to e.g. external noise

It's interesting that you describe it this way, because on this usage, the scenario described in the OP, where a controlled preparation is made of an entangled state of two qubits but one qubit is not measured, is not an instance of decoherence. But the OP claims it is.

So now I'm somewhat confused as to what the actual usage in the QC community is.

 

[Talisman]

It's interesting that you describe it this way, because on this usage, the scenario described in the OP, where a controlled preparation is made of an entangled state of two qubits but one qubit is not measured, is not an instance of decoherence. But the OP claims it is.

So now I'm somewhat confused as to what the actual usage in the QC community is.

Well, there are sub-communities within QC, based on specific implementation. Of course NMR-based labs will understand it to be T1 and T2 relaxation. Now that I've read up on those (both in N&C and Wikipedia), I see why they (T2 in particular) are described as loss of polarization information. At the same time, the example in the "mathematical details" section of Wikipedia (here) covers the more general case of taking a partial trace over the environment, which leads to the aforementioned effects regardless of whether its state is known or not (though as we've beaten to death here, of course it is generally not, given the number of DOF involved). In theoretical QC, this seems to be a common example given to students.

For me, it is useful to understand both models. I can see this may not be true for others, and I do not wish to press the issue.

 

[Talisman]

It's interesting that you describe it this way, because on this usage, the scenario described in the OP, where a controlled preparation is made of an entangled state of two qubits but one qubit is not measured, is not an instance of decoherence. But the OP claims it is.

Perhaps I should be more clear here. I agree that nobody in their right mind actually prepares an entangled state, only to "lose" one of the partners, so as to make the other look incoherent, and then cries "decoherence." But using a well-defined state (like the one given here) exemplifies the essential problem described in the "mathematical details" section cited above in the simplest way possible, for ease of understanding. It demonstrates why we lose coherence in the first particle if we ignore the second, whether that ignorance is fundamental (e.g., inability to measure the environmental state) or contrived (e.g., simply throwing it away to prove a point).

It is a pedagogical tool, and I will be more careful to call it out as such in the future, since it apparently leads to confusion.

 

[f95toli]

It's interesting that you describe it this way, because on this usage, the scenario described in the OP, where a controlled preparation is made of an entangled state of two qubits but one qubit is not measured, is not an instance of decoherence. But the OP claims it is.

So now I'm somewhat confused as to what the actual usage in the QC community is.

That was sort of my point, I don't think anyone who works on QC today would use the word in the way the OP used it. This is why I keep pointing out that -in the way the word is used in QC or say spin physics (NMR, ESR etc)- there is no direct link between decoherence and entanglement. since you can certainly have decoherence in a single system (coupled to suitable environment). Models that e.g. describe decoherence as being caused by entanglement with a measurement device obviously have their uses; but I am not sure they make much sense in situations where your T1 (and therefore T2) is limited by say dielectric losses (which is frequently .the case for solid-state qubit).
I also don't quite see how say decoherence due to the Purcell effect (another important "engineering" consideration for quantum systems) would be modelled?.

 

[f95toli]

The references in this paper give the 10th Anniversary Edition of Nielsen & Chuang as being published in 2011, which would mean the original edition was published in 2001.

Indeed, the book is ancient by QC standards; the introductory chapters covering the basic QM and math are still great, but the rest of the book is no longer very useful.

 

[PeterDonis]

the book is ancient by QC standards

Yes, but not by decoherence standards.

 

[Talisman]

For whatever it's worth, I went and revisited Zurek's original paper (or at least, one of the originals) here: https://arxiv.org/abs/quant-ph/0306072

His example is to start with a system-detector state:
$$|\uparrow\rangle|d_{\uparrow}\rangle + |\downarrow\rangle|d_{\downarrow}\rangle$$

And then entangle it with an environment state:
$$|\uparrow\rangle|d_{\uparrow}\rangle|E_0\rangle + |\downarrow\rangle|d_{\downarrow}\rangle|E_1\rangle$$

With the only requirement being that $\langle E_0|E_1\rangle = 0$ (i.e., the environment is able to distinguish the states). Wherever they came from, the key point is that those DOF are no longer accessible. Then, tracing over them, we lose the off-diagonal elements.

 

[PeterDonis]

Zurek's original paper (or at least, one of the originals)

This isn't one of his original papers; they were published in the early 1980s. This, as the initial text states, is a "revisit" of a review article he wrote for Physics Today in 1991, when he felt that the field had developed enough for him to write such a review.

His example

Which specific equations in the paper are you referring to?

 

[Talisman]

This isn't one of his original papers; they were published in the early 1980s. This, as the initial text states, is a "revisit" of a review article he wrote for Physics Today in 1991, when he felt that the field had developed enough for him to write such a review.Which specific equations in the paper are you referring to?

Ah. The equations are identical to his 1991 paper, but I did not realize he had (and cannot find) earlier ones.

Equation 13, p.10.

 

[PeterDonis]

Equation 13, p.10.

Ok, so if I try to apply this equation to the scenario in your OP, which things in the scenario correspond to which terms in the equation?

 

[PeterDonis]

I did not realize he had (and cannot find) earlier ones.

The earlier ones might not be easily findable online, since they were published in the primitive times before the Internet.

 

[Demystifier]

You can find the same explanation here (in the section titled "Decoherence") from Scott Aaronson.

Excellent!

 

[Demystifier]

Or, as Demystifier says here: https://www.physicsforums.com/threads/irreversibility-vs-reversibility.909761/
When it becomes "irreversible in practice" depends on the technology available to you.

Incidentally, the ocean analogy is used also by Aaronson to explain the idea of hidden variables. https://www.scottaaronson.com/democritus/lec11.html

 

[Talisman]

Ok, so if I try to apply this equation to the scenario in your OP, which things in the scenario correspond to which terms in the equation?

Start with a pure state (the system + detector in Zurek's example, or the single qubit in mine). Maximally entangle it (with E in Zurek's case, or a second qubit in mine). If you now ignore / discard the second system, the first must be modeled as a mixed state. The off-diagonal terms "vanished." If you somehow do manage to track down and measure all the environmental DOF thereafter, you will have enough information to reconstruct those terms, but in any real-world scenario this is impossible, so you are stuck treating it classically.

 

[PeterDonis]

Start with a pure state (the system + detector in Zurek's example, or the single qubit in mine).

A single qubit can't be a system + detector, because a detector, by definition, must be able to register a macroscopic result that a human can perceive. Zurek's description of a measurement has two stages: environment-induced decoherence is the second. The first is entanglement of the system to be measured (which could be a qubit) with the detector (which can't, for the reason given above).

I know you said that you intend your example as pedagogy, not as an actual description of a real measurement, but good pedagogy still has to include all of the essential features of the thing it's describing. That includes the macroscopic nature of the detector.

Maximally entangle it

As I understand Zurek, it is not necessary that the entanglement with the environment be maximal. All that is necessary is that the environment states that correspond to different measurement results are orthogonal.

 

[Talisman]

A single qubit can't be a system + detector, because a detector, by definition, must be able to register a macroscopic result that a human can perceive. Zurek's description of a measurement has two stages: environment-induced decoherence is the second. The first is entanglement of the system to be measured (which could be a qubit) with the detector (which can't, for the reason given above).

I know you said that you intend your example as pedagogy, not as an actual description of a real measurement, but good pedagogy still has to include all of the essential features of the thing it's describing. That includes the macroscopic nature of the detector.

Sure, that's fair. This is physicsforums, after all, and not computerscienceforums. CS people (like Aaronson) tend to look for the simplest example that captures the interesting mathematical details, even if it loses important physical details, and that can indeed be problematic.

As I understand Zurek, it is not necessary that the entanglement with the environment be maximal. All that is necessary is that the environment states that correspond to different measurement results are orthogonal.

I don't know if this is also a definitional thing, but the way it was taught to me, entanglement with orthogonal states implies maximality.

 

[PeterDonis]

the way it was taught to me, entanglement with orthogonal states implies maximality.

For entanglement of two qubits, I believe that follows from the definition of maximal entanglement in terms of Von Neumann entropy.

For entanglement of a system + detector with an environment containing a huge number of degrees of freedom, however, I don't think orthogonality of the environment states (which won't be single states but huge subspaces of the environment Hilbert space) implies maximality of entanglement.