Hidden-variable theorems for real experiments

Physical Review Letters

Volumn 86, Issue 20, 2001, Pages 4427-4430

  Simon, Christoph ^a,b   Brukner, Časlav ^a   Zeilinger, Anton ^a  

^a UNIVERSITY OF VIENNA   (Austria)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION THEORY; RANDOM PROCESSES; SET THEORY; THEOREM PROVING;

KOCHEN-SPECKER THEOREM;

QUANTUM THEORY;

EID: 0035858497     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.86.4427     Document Type: Article

References (22)

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10. n, which is then again tested on a random sample. This assumes that it is possible for the observer to obtain representative samples. This means that there should be no correlation between the hidden variables of the system under study and the observer's choice which observable to measure. For an experiment where a physical random number generator was used in order to determine the choice of observable to be measured, see G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 81, 5039 (1998). It is never possible to exclude "conspiracy-type" hidden-variable theories where the decision of the observer which observable to measure is determined by the hidden variables (of the world) in such a way that it is impossible for him to obtain representative samples.
11. In the present paper we do not discuss stochastic hidden-variable theories explicitly. This does not limit the generality of the results derived because the existence of a stochastic local or noncontextual hidden-variable model for a given physical system implies that also an underlying deterministic local or noncontextual model can be constructed which reproduces the probabilities of the stochastic model. Therefore, e.g., ruling out all possible noncontextual deterministic hidden-variable models implies ruling out all possible noncontextual stochastic models as well. A stochastic hidden-variable theory is noncontextual if for every possible value of the hidden variables the probability to find a certain result for a given observable does not depend on which other observables are measured jointly, and joint probabilities for several observables are simply obtained by multiplication of the probabilities for single observables. Note that because of this last requirement quantum mechanics is not a noncontextual "hidden-variable" theory.
12. In the ideal case one could define noncontextuality in such a way that the predetermined value of some quantum mechanical observable X is required to be independent of the simultaneously measured observables only if they exactly commute with X, i.e., only for ideal von Neumann measurements. In practice observables corresponding to precise directions do not have an operational meaning. It is evident that this weaker form of noncontextuality cannot be tested experimentally.
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