Influence of strong measurements in a Two Slit Interferometer

[Marilyn67]

TL;DR Summary

Thinking on a Young-Wheeler experiment, weak measurements, strong measurements, a 2011 paper, and alice and bob

Hello,

I am interested in weak measures since I discovered this paper:

https://arxiv.org/ftp/arxiv/papers/1206/1206.6224.pdf
I understood that retro-causality is only an interpretation and that's not more exploitable than the famous experiments of quantum gum delayed choice.

In fact, we don't control the result of the measurement, the correlations have always been made afterwards, and therefore, there is no communication as in the classical sense .

In first, we have a remarkable result, with correlations between strong measurements and weak measurements which don't disturb the system, but the counterpart is : no control of the measure.
(We never control the measure, of course, but I continue my development)

Then, there is this famous Wheeler thought experiment like here :

https://en.wikipedia.org/wiki/Wheeler's_delayed-choice_experiment

There is no way by which any given photon could have been determined to have arrived from one or the other of the double slits. However, if the detection screen is removed the wavefunctions on each path will superimpose on regions of lower and lower amplitudes, and their combined probability values will be much less than the unreinforced probability values at the center of each path. When telescopes are aimed to intercept the center of the two paths, there will be equal probabilities of nearly 50% that a photon will show up in one of them. When a photon is detected by telescope 1, researchers may associate that photon with the wavefunction that emerged from the lower slit. When one is detected in telescope 2, researchers may associate that photon with the wavefunction that emerged from the upper slit. The explanation that supports this interpretation of experimental results is that a photon has emerged from one of the slits, and that is the end of the matter.

Thus, secondly, the choice to measure the wave behavior (screen) or the corpuscular behavior of light (telescope T1 or T2) seems to determine which slit passes the photon (F1, F2, or F1-F2), but the counterpart is : no measurement possible upstream (directly in F1 or F2), otherwise we have a collapse of the wave function.

So I asked myself the question :

What would happen if we repeated Wheeler's famous thought experiment, (Gedankenexperiment as Einstein said) and that we decided to make the appropriate weak measures in F1 and F2, so as not to cause the collapse of the wave function ?

What would we get as results / correlations ?

I continued to search and I found this paper:

http://www.kiroku.riec.tohoku.ac.jp/simon/quantum/science-2-slit.pdf

I know there have been several debates in PF from that experience as here :

https://www.physicsforums.com/threads/a-question-about-two-slits-experiment.874283/
However, I didn't find the answer to my question that really more complex, so I decided to open a new discussion.

Indeed, I read the paper whose link was in the discussion :

http://www.tcm.phy.cam.ac.uk/~mdt26/talks/towler_weak_measurements.pdf

I understood correctly :

A strong measurement reveals a property of an individual system, but a weak measurement only reveals a property of a large statistical ensemble of equally prepared systems. A weak measurement says nothing about an individual system.

Ok

But my problem is this:

We all know that the probabilities of impact in a point if we observe in F1 or F2 are different from the probabilities of impact at the same point if we observe the screen :

P1 + P2 = |a1|² + |a2|²

is different from

P12 = |a1 +a2|²

(a = amplitude of probability)

That's the question (finally !) :

The average trajectories in the experiment should be different, dependent that we make a strong measurement or we don't make a strong measurement, and thus affect the weak measure according to the arbitrary choice of the experimenter to place a screen or not.

How to reconcile the no-go theorem with the strange possibility that BOB, which make a series of strong measurements (a screen = 1 or no screen = 0, throughout the series), can communicate with ALICE, which systematically make a series of weak measurements (slits), schematically of course, by using the protocol of the experiment described on the paper ?

(we can have a set of several ensemble of equally prepared systems simultaneously on the same table).

I admit that my question is difficult to ask and I often have trouble doing myself understood, so in advance, excuse me for this long post, (and my english !) but this problem don't let me sleep !

See you soon,

Maryline

 

[charters]

What would happen if we repeated Wheeler's famous thought experiment, (Gedankenexperiment as Einstein said) and that we decided to make the appropriate weak measures in F1 and F2, so as not to cause the collapse of the wave function ?

What you want is discussed here: https://arxiv.org/abs/1304.7474.

The average trajectories in the experiment should be different, dependent that we make a strong measurement or we don't make a strong measurement, and thus affect the weak measure according to the arbitrary choice of the experimenter to place a screen or not.

This doesn't make sense exactly how you wrote it, but I think I know what you mean. And yes, the weak measurement results do change depending on the choice of final strong measurement and post-selection.

How to reconcile the no-go theorem with the strange possibility that BOB, which make a series of strong measurements (a screen = 1 or no screen = 0, throughout the series), can communicate with ALICE, which systematically make a series of weak measurements (slits), schematically of course, by using the protocol of the experiment described on the paper ?

FTL communication is impossible because Alice cannot see anything but the basic expectation value until Bob sends her the postselection data.

 

[Marilyn67]

Hello charters,

Thank you for your answer,

What you want is discussed here: https://arxiv.org/abs/1304.7474.

Thank you for the link !
I have only read the abstract, but I will read the document closely.

This does not make sense exactly how you wrote it, but I think I know what you mean. And yes, the weak measurement results do change depending on the choice of final measurement and post-selection.

Ok.

FTL communication is impossible because Bob sends her the postselection data.

There, I don't understand.

I know that in Marlan Scully's delayed choice quantum gum experiment, the communication is "scrambled," and Bob has to pass information through the classical channel to Alice to reconstruct the signal. Ok.

But it seems to me that here it's different :
You say it yourself above:

The weak measurement results do change depending on the choice of final measurement and post-selection.

Are you sure that in this experiment where Alice make weak measurements, she sees only a basic expectation value ?

Here, the measure is the measure, and we can't change it once it has been made : It's the same single photon for Bob and Alice, while the experience of Marlan Scully uses pairs entangled photons.

This situation doesn't it deserve to be studied in greater depth ?
In advance, thank you for your answer !

Cordially,

Maryline

 

[charters]

The weak measurement results do change depending on the choice of final measurement and post-selection.

But this is all a postselection/filtering/sub-sampling effect.

Are you sure that in this experiment where Alice make weak measurements, she sees only a basic expectation value ?

Yes

Here, the measure is the measure, and we can't change it once it has been made : It's the same single photon for Bob and Alice,

No, you cannot do weak measurements without a large sample of photons. Then, when Bob sends Alice the report of his chosen measurement basis and which results he got, Alice can see patterns in her corresponding sub-samples, which is what reveals the weak value measurement.

 

[Marilyn67]

Hello charters,

No, you cannot do weak measurements without a large sample of photons. Then, when Bob sends Alice the report of his chosen measurement basis and which results he got, Alice can see patterns in her corresponding sub-samples, which is what reveals the weak value measurement.

I am very impressed by the speed and quality of your answers!

I have a last question:
To have multiple samples, does that change anything if, instead of repeating the process multiple times, Bob and Alice collect all the samples at once on several identical test benches on the same table?

I think you'll tell me it doesn't change anything...

I wish you a good evening !

cordially
Maryline

 

[charters]

To have multiple samples, does that change anything if, instead of repeating the process multiple times, Bob and Alice collect all the samples at once on several identical test benches on the same table?

In theory it shouldn't matter, but Alice will still only see the weak value pattern in the average of all benches post-selected for a given outcome of Bob's strong measurement. Alice's result on any individual bench will generally not give the actual weak value.

In reality, an n=1 weak measurement will be too faint of a signal to be readable anyway. You won't even be sure the weak detector actually detected anything successfully.

 

[Marilyn67]

Hello charters,
Thank you very much for your answer !

In theory it shouldn't matter, but Alice will still only see the weak value pattern in the average of all benches post-selected for a given outcome of Bob's strong measurement.

What do you mean by "weak value pattern" ?

Alice's result on any individual bench will generally not give the actual weak value.
In reality, an n=1 weak measurement will be too faint of a signal to be readable anyway. You won't even be sure the weak detector actually detected anything successfully.

I don't think about an individual bench but all the benches giving an average value n = 1 for all the weak measurements make by Alice.

Cordially
Maryline

 

[charters]

What do you mean by "weak value pattern" ?

Just whatever result the weak measurement device shows after filtering by postselection.

 

[Marilyn67]

Good evening charters,

Thank you for your response and your patience.
I think I understood why FTL communication is impossible here too.
I need to read your document better

Thanks again
Maryline