A delayed choice experiment with a paradox. What did I do wrong?

  • Thread starter Fredrik
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Hello Eye_in_the_Sky,

as far as I understood, Fredrik's experiment isn't about quantum-erasure,
but rather the opposite. "Quantum erasure" is the phenomenon, that you can erase the which-way-information, right?

But in Fredrik's gedankenexperiment, we do the opposite, we try to gain which-way-information by taking away the upper half silvered mirror.

I think the question is really what happens in the inner Mach-Zehnder-system, that is, what kind of statistics do we get there?

In my opinion, the interference is destroyed although we take the upper mirror away after it made click at the inner detectors. I know, that seems strange, but I got this impression after reading about the delayed quantum erasure experiments.

What do you think is the statistics at the inner detectors in Fredrik's gedankenexperiment?
 
Edgardo said:
... as far as I understood, Fredrik's experiment isn't about quantum-erasure, but rather the opposite ... in Fredrik's gedankenexperiment ... we try to gain which-way-information by taking away the upper half silvered mirror.
First look at Fredrik's setup without the upper half-silvered mirror in place; call this new setup E1. Then put back the upper half-silvered mirror to return to Fredrik's setup; call this setup E2.

Next, consider the following two statements:

S1) In setup E1 the detection ratio for the lower detectors is 50:50 ;

S2) In setup E2 the detection ratio for the lower detectors is 100:0 .

For the moment, let us assume that both of these statements are true. Then, E2 – when compared to E1 – has the character of a "quantum-erasure" experiment, and the upper half-silvered mirror plays the role of the "eraser".
___________
Edgardo said:
What do you think is the statistics at the inner detectors in Fredrik's gedankenexperiment?
50:50. Statement S2 is false.
 

Fredrik

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Thanks for the answer Eye_in_the_Sky. You've given me a lot to think about. I've been thinking about it a lot since I read it, but I need to think some more...
 
a concise summary

Below is a generalization based upon what I have seen and found regarding Quantum Erasure.

Following that are some comments in connection with Fredrik's thought experiment.
_____________

In all of these "quantum-erasure" experiments, the which-way information of the signal is "erased" by means of the insertion of a new element – called the "eraser" – into an existing setup. The insertion-point of that "eraser" can be in one of two places, depending upon the type of setup involved; that is, the "eraser" can be inserted:

1) in the signal beam;

or

2) not in the signal beam, but in some other beam consisting of a signal "counterpart" which exists in an appropriate state of entanglement with the signal.

In a type-2 scenario, the are two important points to take note of:

2a) the "eraser" must be something which 'collapses' the wavefunction;

2b) the statistics at the signal detector(s) are the same whether or not the "eraser" has been inserted.

Regarding 2b, the data set at the signal detector(s) must be compared with another data set generated at (or after) the "eraser" in order to be able to infer that a 'change' of some kind has occurred in the signal on account of the "erasing" action.
_____________

In connection with Fredrik's thought experiment (which was of the type-2 genre), in the original analysis it was found that condition 2b was violated. In that analysis, however, it was implicitly assumed that a half-silvered mirror (serving as the "eraser") is something which 'collapses' the wavefunction ... which, of course, is not true. That is to say, the requirement of 2a was not met, yet implicitly in the original analysis that condition was assumed to be true.

Since 2a does not hold, that setup does not give rise to a "quantum-erasure" scenario.

In more intuitive terms, it seems reasonable to say that, yes, the which-way information of the signal "counterpart" (i.e. the outer "half"-photons) is erased, but, because the "eraser" itself (i.e. the upper half-silvered mirror) does not 'collapse' the wavefunction, that "erasing action" is not (so to speak) 'communicated' to the signal.

From another perspective, one might venture to add that, by inserting the upper half-silvered mirror into the setup, the which-way information of the signal which was present in the entangled signal-"counterpart" has merely been 'thrown away', or in other words ... 'ignored'.
 
Last edited:

Cat

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I haven't studied all the messages carefully, but had a look at the diagram and can predict that you won't actually ever be able to get the 100% to 0% split you expect. Instead, you should find that you get signs of interference effects showing up if you look at the coincidence curve for the two lower detectors.

You might be able to get your predicted effect if you followed the design of, say:

Zou, X Y, Wang, L J and Mandel, L, “Induced coherence and indistinguishability in optical interference”, Physical Review Letters 67, 318 (1991)

If I remember correctly, they took the output from one DC and fed it into the other. They interpreted their effect in terms of indistinguishable paths, but I think there is a much simpler classical explanation: the fact that a single laser is used as main input to both DCs means that the output phases are linked to those of this laser but, because the frequency is only half, 50% tend to be linked to "even" laser peaks, 50% to "odd" ones. With the DC's independent, the choice of even or odd is independent, but when they are linked this forces them to make the same choice.

There was an article that included the experiment (though not my personal explanation!) in Physics Today, or was it Physics World. See:

Greenberger, Daniel and Anton Zeilinger, “Quantum theory: still crazy after all these years”, Physics World, 33-38, September 1995

or maybe

Greenberger, D M, Horne, M A and Zeilinger, A, “Multiparticle interferometry and the superposition principle”, Physics Today, 22-29, August 1993

Cat
 

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