Proof of non-locality indep. of conservation law

[DrChinese]

Well its not a "test" of a Bell Inequality in such a scenario. Actually what happens in practise (except in the cases that violation of local realism IS being tested) is that state tomography is done in a manner such as you described - multiple runs with one pair of settings, multiple ones at another and so on. The reconstructed density matrix is subjected to certain maximum-likelihood estimation to produce a "physical" density matrix (i.e. one with positive eigenvalues, which is not what the tomography always gives!), and then sometimes from this reconstructed density matrix a value that would have occurred were one to try and violate the inequality is computed. This latter part is simply a way of demonstrating "how entangled" one's state was with a single parameter, but of course has nothing to do with "testing" Bell's theorem...

Tez,

You are obviously extremely familiar with Bell tests and the discussions of loopholes.

In your personal opinion: why does a "loophole free" test of Bell's Inequality rate such interest? I.e. why do you think it is important? I never see discussions of "loophole free" tests of any other phenomena (you name it: speed of light, existence of neutrinos, etc.). And I certainly can't recall any other controversial experiment which requires so many variables to be held constant simultaneously: switching mid-flight, random settings, space-like separation, high visibility, etc.

-DrC

-----------

P.S. By the way, the comments under the dashed line in my prior 2 posts were not aimed at you or your comments.

 

[Tez]

Tez,
In your personal opinion: why does a "loophole free" test of Bell's Inequality rate such interest? I.e. why do you think it is important? I never see discussions of "loophole free" tests of any other phenomena (you name it: speed of light, existence of neutrinos, etc.).

Its a good question. I think it is ok for me to post this - it is a part of an old email I saved, containing a statement from Asher Peres, who incidentally IMO wrote far and away the best modern textbook on QM, but who was also a great human being. And it seems he agreed with you! (note: Asher was writing it for the editors of a certain journal, not for me!)

>
> May we seek your advice on this manuscript? We have been turning
> down many papers on how one might test local realism, feeling guided
> by a wise statement by the late Asher Peres:
>
> "In 1964, John Bell proved that local realistic theories led to an
> upper bound on correlations between distant events (Bell's
> inequality) and that quantum mechanics had predictions that violated
> that inequality. Ten years later, experimenters started to test in
> the laboratory the iolation of Bell's inequality (or similar
> predictions of local realism). No experiment is perfect, and various
> authors invented 'loopholes' such that the experiments were still
> compatible with local realism. Of course nobody proposed a local
> realistic theory that would reproduce quantitative predictions of
> quantum theory (energy levels, transition rates, etc.).
>
> This loophole hunting has no interest whatsoever in physics. It
> tells us nothing on the properties of nature. It makes no prediction
> that can be tested in new experiments. Therefore, I recommend not to
> publish this paper in [XXXXX]. Perhaps it is suitable for
> a journal on the philosophy of science."
>

So why are people even attempting a loophole free test? I think the best explanation is to do with the psychology of the community involved. These people (me included I guess) generally think that Bell's theorem is the most important feature of modern physics in some sense: If I had to choose which "surprising" feature of physics would most likely still have "relevance" in 1000 years time, I'd probably pick Bell's theorem. Why? Because I think all creatures evolve to think of locality as an essential feature of their worldview. Even if we have a deeper theory in which all this emerges more naturally, it'll still be more counterintuitive than the Relativity principle and so on.

So - "psychology of the community" not really a good answer I realize. (Though a large percentage of science is driven by the whims of the folks getting the funding.)

Here is the rough scheme of an answer I would give if I was trying to convince editors of a journal that my experiment closing the detector loophole was significant:

It is generally believed that Quantum Computation requires entanglement to achieve its enhancement over its classical counterpart. Thus a quantum computer will be able to violate a Bell Inequality "for real" - i.e. with detectors that are efficient enough. (I guess another way of seeing this is that if a quantum computation is incapable of demonstrating nonlocality then it seems plausible that the LHV "underlying it" is simulatable on a classical computer). Thus closing the detector loophole is likely to be a significant technological advance for certain quantum computational architectures.

The problem with this is that the detector loophole was already closed in ion traps (without the ions being spacelike separated of course...). However it certain han't been closed for many versions of optical quantum computation...

 

[DrChinese]

Its a good question. I think it is ok for me to post this - it is a part of an old email I saved, containing a statement from Asher Peres, who incidentally IMO wrote far and away the best modern textbook on QM, but who was also a great human being. And it seems he agreed with you! (note: Asher was writing it for the editors of a certain journal, not for me!)
>
> May we seek your advice on this manuscript? We have been turning
> down many papers on how one might test local realism, feeling guided
> by a wise statement by the late Asher Peres:
>
> "In 1964, John Bell proved that local realistic theories led to an
> upper bound on correlations between distant events (Bell's
> inequality) and that quantum mechanics had predictions that violated
> that inequality. Ten years later, experimenters started to test in
> the laboratory the iolation of Bell's inequality (or similar
> predictions of local realism). No experiment is perfect, and various
> authors invented 'loopholes' such that the experiments were still
> compatible with local realism. Of course nobody proposed a local
> realistic theory that would reproduce quantitative predictions of
> quantum theory (energy levels, transition rates, etc.).
>
> This loophole hunting has no interest whatsoever in physics. It
> tells us nothing on the properties of nature. It makes no prediction
> that can be tested in new experiments. Therefore, I recommend not to
> publish this paper in [XXXXX]. Perhaps it is suitable for
> a journal on the philosophy of science."
>
So why are people even attempting a loophole free test? I think the best explanation is to do with the psychology of the community involved. These people (me included I guess) generally think that Bell's theorem is the most important feature of modern physics in some sense: If I had to choose which "surprising" feature of physics would most likely still have "relevance" in 1000 years time, I'd probably pick Bell's theorem. Why? Because I think all creatures evolve to think of locality as an essential feature of their worldview. Even if we have a deeper theory in which all this emerges more naturally, it'll still be more counterintuitive than the Relativity principle and so on.

So - "psychology of the community" not really a good answer I realize.

Thanks for taking time for such a well-considered answer to my question - and especially for sharing the Peres comment. Hearing your thoughts clears up a few things that were confusing to me.

 

[DrChinese]

Its a good question. I think it is ok for me to post this - it is a part of an old email I saved, containing a statement from Asher Peres, who incidentally IMO wrote far and away the best modern textbook on QM, but who was also a great human being. And it seems he agreed with you! (note: Asher was writing it for the editors of a certain journal, not for me!)
>
> May we seek your advice on this manuscript? We have been turning
> down many papers on how one might test local realism, feeling guided
> by a wise statement by the late Asher Peres:
>
> "In 1964, John Bell proved that local realistic theories led to an
> upper bound on correlations between distant events (Bell's
> inequality) and that quantum mechanics had predictions that violated
> that inequality. Ten years later, experimenters started to test in
> the laboratory the iolation of Bell's inequality (or similar
> predictions of local realism). No experiment is perfect, and various
> authors invented 'loopholes' such that the experiments were still
> compatible with local realism. Of course nobody proposed a local
> realistic theory that would reproduce quantitative predictions of
> quantum theory (energy levels, transition rates, etc.).
>
> This loophole hunting has no interest whatsoever in physics. It
> tells us nothing on the properties of nature. It makes no prediction
> that can be tested in new experiments. Therefore, I recommend not to
> publish this paper in [XXXXX]. Perhaps it is suitable for
> a journal on the philosophy of science."
>
So why are people even attempting a loophole free test? I think the best explanation is to do with the psychology of the community involved. These people (me included I guess) generally think that Bell's theorem is the most important feature of modern physics in some sense: If I had to choose which "surprising" feature of physics would most likely still have "relevance" in 1000 years time, I'd probably pick Bell's theorem. Why? Because I think all creatures evolve to think of locality as an essential feature of their worldview. Even if we have a deeper theory in which all this emerges more naturally, it'll still be more counterintuitive than the Relativity principle and so on.

Thanks for taking time for such a well-considered answer to my question - and especially for sharing the Peres comment. Hearing your thoughts clears up a few things that were confusing to me.

 

[rlduncan]

Is more of the data given by N. David Mermin in the article "Is the Moon there when nobody looks? Reality and the quantum theory" available online for easy access to anyone interested in analyzing it further.