COMPARISON OF CHSH AND CH74 TESTS[i]

 

 

CHSH

CH74

Source

Attributed to CHSH 1969[ii] paper.  Never in fact supported by authors.

Best derivation: appendix to CH74[iii] paper (reproduced in quant-ph/9903066).

Experimental design

Two-channel[iv]:

Single-channel:

 

– 2 £ S £ 2

S < 0

Formula

 

 

where

and

where

and ,

the symbol ¥ indicating absence of polariser[v]

Used

Variants of this and the related “visibility” test have been used in the majority of experiments since 1982.

Variants were used in all experiments up to 1982.

Advantages

Relatively easy to violate.

Does not depend on fair sampling.

Disadvantages

Depends on the fair sampling assumption, which implies among other things:

Assumes “no enhancement”

Hard to violate.

 



[i] This page is based on an appendix to: C. H. Thompson, “Setting the Record Straight on Quantum Entanglement”, http://freespace.virgin.net/ch.thompson1/Papers/TheRec/TheRecord.htm/

[ii] J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, Proposed experiment to test local hidden-variable theories, Physical Review Letters 23, 880-884 (1969)

[iii] J. F. Clauser and M. A. Horne, Experimental consequences of objective local theories, Physical Review D, 10, 526-35 (1974)

[iv] Though intended for use with two-channel detectors, the CHSH test can, with a little ingenuity, be used for single-channel experiments.  See for example P. G. Kwiat et al.,  “Ultrabright source of polarization-entangled photons”, Phys. Rev. A 60 (2), R773-R776 (1999), http://arXiv.org/abs/quant-ph/9810003

[v] Though the derivation of the CH74 inequality is in terms of probabilities, the actual test (as Clauser and Horne recognised) could be conducted on the raw counts, since the limit is zero.  Normalising by division by N(¥,¥) is for convenience when comparing experiments.