I What does decoherence have to do with phases?

[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.

 

[Talisman]

Here is Artur Ekert, a major figure in QIS, giving the single-qubit + environment example a year ago:

The textbook version is here https://qubit.guide/12.2-decoherence-and-interference.html

For better or worse, this usage does indeed seem to well-established in this particular field.

 

[kith]

As others have noted, "decoherence" is used differently in different communities. I've found the section "A Few Words on Nomenclature" in Klaus Hornberger's 2009 lecture notes Introduction to decoherence helpful in the past. It gave me an overview of the different usages of "decoherece" and how it relates to similar concepts like "dephasing".