Measurement Possibilities: The Role of Efficiency and Distance in Bell's Theorem

[MikeGomez]

Quote from this recently posted article.
http://www.nature.com/news/physics-bell-s-theorem-still-reverberates-1.15435

“Quantum theory does not predict the outcomes of a single experiment, but rather the statistics of possible outcomes.”

My question is not in regards to the statistics of the correlations of relative angle measurements, but rather with the statistics of successfully making a measurement.

For each and every entangled pair, is it guaranteed that Bob and Alice will each always be able to make a measurement, or do measurements of a certain relative angle require many trials due to the possibility that either Bob or Alice (or both) might not detect their particle?

 

[atyy]

In theory, quantum mechanics allows Bob and Alice make successful measurements every time. In practice, this is not achieved, and causes a "detection loophole", meaning that the experiments don't conclusively show that reality is nonlocal. A recent report indicates some progress in closing this loophole http://arxiv.org/abs/1306.5772.

 

[MikeGomez]

Thanks. The articles claims a final detection efficiency of 75% +- 2%. I would have naively guessed that the detection efficieny would have to be much greater, perhaps at least 90%, in order to rule out local realism.

 

[Water nosfim]

Thanks. The articles claims a final detection efficiency of 75% +- 2%. I would have naively guessed that the detection efficieny would have to be much greater, perhaps at least 90%, in order to rule out local realism.

The thing is , when you get down in dimension you get only persenteg

 

[Nugatory]

Thanks. The articles claims a final detection efficiency of 75% +- 2%. I would have naively guessed that the detection efficieny would have to be much greater, perhaps at least 90%, in order to rule out local realism.

The detector efficiencies can be and are evaluated as part of setting up and calibrating the experiment. As long as the inefficiencies are somewhat randomly distributed, we can figure the probability that they will skew the result by a given amount, and the more data points we gather the smaller this effect is. Thus, longer runs can be used to compensate for known detector inefficiencies.

There is a class of loopholes that are sometimes called "conspiratorial", and these could invalidate the results. For example, if the detectors and particles were to malfunction one way during the calibration/setup of the experiment and another way during the operation of the experiment, or if the settings of the detectors and the initial state of the particles were to all be determined in advance... Then it would be possible to take advantage of the detection loophole to construct a local realistic theory that violates the inequality, as the particles and detectors conspire to report a biased subset of the total number of pairs that come by.

However, checking for and minimizing this sort of systemic bias is bread-and-butter for experimentalists. So many experiments have been done and so many results replicated by so many different teams using different techniques, that at this point any simple conspiratorial theory based on detector inefficiencies would be at least as fantastic as just accepting that nature doesn't respect Bell's inequalities.
(There are more sophisticated conspiratorial theories - google for "superdeterminism T'Hooft" for an example).

 

[DrChinese]

In theory, quantum mechanics allows Bob and Alice make successful measurements every time. In practice, this is not achieved, and causes a "detection loophole", meaning that the experiments don't conclusively show that reality is nonlocal. A recent report indicates some progress in closing this loophole http://arxiv.org/abs/1306.5772.

Not to disagree with your always esteemed comments, but...

Whether someone views existing experiments as "conclusive" is something of a subjective standard. For all practical purposes, Bell experiments have been reasonably conclusive at least since Weihs et al (1998) which closed the locality "loophole"*. And you could equally say General Relativity has still not been conclusively proven by experiment because it is still being tested. When do you stop testing any theory? Closing all Bell loopholes* simultaneously is the new goal, but is not strictly necessary.

Re the OP's comment about detection: atyy's citation is about closing the detection loophole is for photons. The detection loophole itself was closed over a decade ago by Wineland et al (he won the Nobel for this and other experiments):

http://www.nature.com/nature/journal/v409/n6822/full/409791a0.html

Experimental violation of a Bell's inequality with efficient detection (2001)

M. A. Rowe, D. Kielpinski, V. Meyer1, C. A. Sackett, W. M. Itano, C. Monroe & D. J. Wineland

Abstract: "Local realism is the idea that objects have definite properties whether or not they are measured, and that measurements of these properties are not affected by events taking place sufficiently far away. Einstein, Podolsky and Rosen used these reasonable assumptions to conclude that quantum mechanics is incomplete. Starting in 1965, Bell and others constructed mathematical inequalities whereby experimental tests could distinguish between quantum mechanics and local realistic theories. Many experiments have since been done that are consistent with quantum mechanics and inconsistent with local realism. But these conclusions remain the subject of considerable interest and debate, and experiments are still being refined to overcome ‘loopholes’ that might allow a local realistic interpretation. Here we have measured correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality. Our measured value of the appropriate Bell's ‘signal’ is 2.25 ± 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called ‘detection’ loophole."


*Loophole being something of a misnomer due to a variety of connotations.

 

[atyy]

@DrChinese, you and anyone else are welcome to disagree with my comments any time!

Thanks for the pointers to the Weihs et al (1998) and Rowe et al (2001) work!

 

[MikeGomez]

Thanks Nutagory and DrChinese.

I’ve read in the literature about simultaneously closing all the loopholes. Is there any chance that the loopholes themselves represent non-commuting variables such that it might not be possible to close them all at the same time, due to the HUP?

 

[Nugatory]

Thanks Nutagory and DrChinese.

I’ve read in the literature about simultaneously closing all the loopholes. Is there any chance that the loopholes themselves represent non-commuting variables such that it might not be possible to close them all at the same time, due to the HUP?

No. There's no theoretical impediment to setting up detectors of sufficient efficiency that can be switched from one setting to another with sufficient speed and then situating them at sufficient distance to exclude all non-conspiratorial explanations of violation, to whatever degree of certainty we require.

 

[stevendaryl]

No. There's no theoretical impediment to setting up detectors of sufficient efficiency that can be switched from one setting to another with sufficient speed and then situating them at sufficient distance to exclude all non-conspiratorial explanations of violation, to whatever degree of certainty we require.

On the other hand, who says that the ultimate explanation for QM will be non-conspiratorial?