Uncollapsing a State: A Fresh Look at the Measurement Problem

[sokrates]

"Uncollapsing" a state?

http://arxiv.org/abs/0806.3547

Seems to be a fascinating idea... It is probably a great experimental achievement for the theory of decoherence - because it basically shows that the collapse of a state is not instantaneous... Moreover, the original state could be recovered before it collapses ?!

This could shed fresh light on the measurement problem.

Ideas?

 

[Hurkyl]

What makes this different from a quantum eraser?

 

[sokrates]

I really don't know what you are addressing here, it is completely irrelevant as to what I have posted.

Hurkyl: I don't see how this connects to Quantum Eraser, I am not very familiar with that, but does it involve recovering a state from collapsing?

 

[bobquantum]

I don't even think its possible to uncollapse a state. The Second Law of thermodynamics states that entropy alsways increases, so basically if you smoke a cigarette, you can put the smoke back into the cigarette.

Hope this helped,
BOB

 

[sokrates]

Well, this is a PRL paper and it was reviewed in Nature if I am not wrong... So whatever they mean by "uncollapsing" is I am sure in agreement with the second law.

Thanks,

 

[DrChinese]

I don't even think its possible to uncollapse a state. The Second Law of thermodynamics states that entropy alsways increases, so basically if you smoke a cigarette, you can put the smoke back into the cigarette.

Hope this helped,
BOB

Strangely, you CAN uncollapse a state. You can collapse/split light via a polarizing beam splitter (PBS) into H and V components, and then recombine those components (which has the effect of "erasing" the measurement from the PBS). If you do this with an entangled photon, the entanglement is restored.

http://www.optics.rochester.edu/~stroud/cqi/rochester/UR19.pdf

I don't believe the experiment as described in Fig. 1 has been performed, at least I don't have a good reference for it.

 

[newbee]

What does "partial collapse" mean? You either make the measurement and collapse or not. Right?

 

[DrChinese]

What does "partial collapse" mean? You either make the measurement and collapse or not. Right?

That would have been a reasonable assumption. But this being a quantum world...

You can un-collapse after collapse. You can collapse some non-commuting pairs while leaving others entangled. And you can have partial collapse (which makes sense given the HUP - delta P * delta Q which presumably could have narrower or wider P or Q in any combination). Did I leave anything out?

 

[javierR]

What makes this different from a quantum eraser?

From pg. 2 of the article (italics mine): "In order for the uncollapsing procedure to work, we
have to erase the information that was already extracted
classically. This distinguishes this measurement-induced
uncollapsing from a “quantum eraser” [10], in which only
potentially extractable information is erased."

 

[javierR]

... it basically shows that the collapse of a state is not instantaneous...
This could shed fresh light on the measurement problem.

I don't see anything in the experiment that says anything about the "collapse" itself...how did you interpret that result? Skimming the article, it appears to be consistent with the principal interpretations of quantum mechanics, and therefore with the usual role of measurement in those interpretations.

Still, an interesting experiment.

 

[Hurkyl]

I'll believe it when I see a clear description of it.

Recall that it's easy to explain the quantum eraser in these terms. For example, the following hypothetical experiment:


We build a measuring circuit as follows:

The circuit consists of a CNOT gate. On input, we feed |0> into the target line and the qubit to be measured on the control line. On output, we route the target line to a "measurement" line. The control line outputs the qubit that was measured.

This device is easily seen to collapse the measured qubit. However, we can build an uncollapsing circuit as follows:

The circuit consists of a CNOT gate. On input, we feed the "measurement" line from the previous circuit onto the target line, and the qubit to be uncollapsed on the control line. On output, we ignore the target line. The control line contains the uncollapsed qubit.

This device is easily seen to reverse the collapse.



My expectation is that the experiment performs a morally similar operation, probably along the following lines:

Between the measuring circuit and the uncollapsing circuit, we attach a partial measurement circuit to measure the "measurement" line. This is the same as the original measurement circuit, except it triggers with probability p. I.E. the transformation it produces is

|a, b\rangle \mapsto \sqrt{p} \, |a, b\rangle + \sqrt{1-p} \, |a+b, b\rangle
(second qubit is control, first qubit is target)
​

This experiment transforms (if I've done the arithmetic correctly) the qubit \psi = a|0\rangle + b|1\rangle into the state with density matrix

\sqrt{1-p} \, \psi \psi^* + \left(1 - \sqrt{1 - p}\right) \left(|a|^2 \, |0\rangle\langle0| + |b|^2 \, |1\rangle\langle1|\right)​

 

[sokrates]

I didn't see this earlier, thank you for the description
It is very clear.