Loopholes in optical Bell test experiments
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Introduction
The "fair sampling" (alias "detection", "efficiency" or "variable detection probability") loophole is, at least among professionals, a well known problem in tests of Bell's theorem, but in real experiments there are several other possiblities that make "local realist" explanations of Bell test violations possible. Each of those discussed below needs to be checked for and screened out before a test violation can safely be said to rule out local realism. Alain Aspect and his team would not have received such acclaim had they not made every effort to make sure they had ruled out all loopholes, but nevertheless, for a realist searching for alternative explanations of the facts, or even for someone trying to apply quantum entanglement, it might be worth their while to ask if some loopholes might not have been as thoroughly closed as the experimenters thought — if, perhaps, quantum theory had suggested they could not be open whereas alternative theories said otherwise.
See also Bell test experiments
There is more than one "Bell test", the ones used in practice being the CHSH, CH74 and "visibility" tests and ones related to these. Many of the loopholes are common to all tests but two important ones are applicable only to certain versions. The fair sampling loophole applies to the CHSH and visibility tests but not to the CH74 one; the "no enhancement" loophole applies to the CH74 test and not to the other two.
Most of the loopholes mentioned here are associated with practical difficulties brought up by Clauser and Horne as endnotes to their seminal 1974 paper (Clauser, 1974). Little else has been published even on the well known loopholes, however, the local realist point of view being currently out of favour. What little there is, is far outweighed by the literature on experimental evidence for quantum entanglement, discussions of its consequences on the assumption that experiments have proved that it really happens, and papers reporting the beginnings of practical applications in quantum computing and quantum cryptography. The existence of loopholes, incidentally, suggests that these applications might be not as dependent on entanglement as their developers think. It could be ordinary correlations causing the observed effects.
The loopholes discussed below are those that might be present in real optical Bell tests. That does not mean to say that in any given experiment they are actually present though, equally, it is possible that more than one may apply. Non-optical Bell test share some of the problems of optical ones but have others in addition.
Practical loopholes
Fair sampling
The "fair sampling assumption" states that the sample of detected pairs is representative of the pairs emitted. The possibility of this not being true comprises the "fair sampling", "detection", "efficiency" or "variable detection probability" loophole. It applies to the CHSH and visibility tests unless detection efficiencies are higher than is currently feasible. It is possible to test experimentally for the sample not being fair by checking the constancy of the total coincidence counts, but the variations expected here are small. The loophole may be widespread, especially in recent tests. The principle behind it can be understood intuitively by means of the Chaotic Ball model devised by Caroline Thompson (Thompson, 1996).
Subtraction of “accidentals”
Adjustment of the data by subtraction of “accidentals”, though standard practice in many applications, can bias Bell tests in favour of quantum theory. After a period in which this fact has been ignored by some experimenters, it is now once again accepted . The reader should be aware, though, that it invalidates many published results. Notable examples in which there were large numbers of accidentals are Aspect's experiments (Aspect, 1981-2) and the early "long-distance" Bell tests conducted in Geneva (Tittel, 1997). These experiments are discussed in (Thompson, 2003).
Failure of rotational invariance
The source is said to be "rotationally invariant" if all possible hidden variable values (describing the states of the emitted pairs) are equally likely. The general form of a Bell test does not assume rotational invariance, but a number of experiments have been analysed using a simplified formula that depends upon it. It is possible that there has not always been adequate testing to justify this. Even where, as is usually the case, the actual test applied is general, if the hidden variables are not rotationally invariant this can result in misleading descriptions of the results. Graphs may be presented, for example, of coincidence rate against the difference between the settings a and b, but if a more comprehensive set of experiments had been done it might have become clear that the rate depended on a and b separately. Cases in point may be Weihs’ experiment (Weihs, 1998), presented as having closed the “locality” loophole, and Kwiat’s demonstration of entanglement using an “ultrabright photon source” (Kwiat, 1999).
Synchronisation problems
There is reason to think that in a few experiments bias could be caused when the coincidence window is shorter than some of the light pulses involved (Thompson, 1997). Experiments that might be affected include one of historical importance — that of Freedman and Clauser (Freedman, 1972) — which used a test possibly not sullied by any of the above possibilities.
Enhancement
The CH74 and related tests are subject to the assumption that there is “no enhancement”, i.e. that there is no hidden variable value for which the presence of a polariser increases the probability of detection. This assumption is considered suspect by some authors, but in practice, in the few instances in which the CH74 inequality has been used, the test has been invalidated by other more evident loopholes such as the subtraction of accidentals.
Double detections
In many experiments the electronics is such that simultaneous ‘+’ and ‘–’ counts from both outputs of a polariser can never occur, only one or the other being recorded. Under quantum mechanics, they will not occur anyway, but under a wave theory the suppression of these counts will cause even the basic realist prediction to yield “unfair sampling”. The effect is negligible, however, if the detection efficiencies are low.
A theoretical loophole: "locality"
A loophole that is notably absent from the above section is the so-called “locality” or “light-cone” one, whereby some unspecified mechanism is taken as conveying additional information between the two detectors so as to increase their correlation above the classical limit. In the view of many realists, this has never been a serious contender. John Bell supported Aspect’s investigation of it (see page 109 of (Bell, 1987)) and had some active involvement with the work, being on the examining board for Aspect’s PhD. Weihs improved upon the test in his experiment of 1998 (Weihs, 1998), but nobody has ever put forward plausible ideas for the mechanism. Its properties would have to be quite extraordinary, as it is required to explain “entanglement” in a great variety of geometrical setups, including over a distance of several kilometers in the Geneva experiments of 1997-8 (Tittel, 1997-8).
References of articles in reputable journals
- Aspect, 1981-2: A. Aspect et al., Phys. Rev. Lett. 47, 460 (1981); 49, 91 (1982); 49, 1804 (1982). Both 1982 articles are available at http://fangio.magnet.fsu.edu/~vlad/pr100/
- Bell, 1987: J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, (Cambridge University Press 1987)
- Clauser, 1974: J. F. Clauser and M. A. Horne, Experimental consequences of objective local theories, Phys. Rev. D 10, 526-35 (1974)
- Freedman, 1972: S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (1972)
- Kwiat, 1999: P.G. Kwiat, et al., Ultrabright source of polarization-entangled photons, Physical Review A 60 (2), R773-R776 (1999)
- Thompson, 1996: C. H. Thompson, The Chaotic Ball: An Intuitive Analogy for EPR Experiments, Found. Phys. Lett. 9, 357 (1996)
- Tittel, 1997: W. Tittel et al., Experimental demonstration of quantum-correlations over more than 10 kilometers, Phys. Rev. A, 57, 3229 (1997)
- Weihs, 1998: G. Weihs, et al., Violation of Bell’s inequality under strict Einstein locality conditions, Phys. Rev. Lett. 81, 5039 (1998) and private correspondence
Other references
- Tittel, 1998: W. Tittel et al., Long-distance Bell-type tests using energy-time entangled photons, (1998)
- Thompson, 1997: C. H. Thompson, Timing, ‘accidentals’ and other artifacts in EPR Experiments (1997)
- Thompson, 1999: C. H. Thompson, Rotational invariance, phase relationships and the quantum entanglement illusion (1999)
- Thompson, 2003: C. H. Thompson, Subtraction of ‘accidentals’ and the validity of Bell tests, Galilean Electrodynamics 14 (3), 43-50 (2003)