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Summary: Security in Quantum Cryptography vs. Nonlocal
Hidden Variables 1
Diederik Aerts
, Marek Czachor,
and Marcin Pawlowski
Centrum Leo Apostel (CLEA) and Foundations of the Exact Sciences (FUND)
Vrije Universiteit Brussel, 1050 Brussels, Belgium
Katedra Fizyki Teoretycznej i Informatyki Kwantowej, Politechnika GdaŽnska, 80-952 GdaŽnsk,
Poland
Abstract. In order to prove equivalence of quantum mechanics with nonlocal hidden-variable the-
ories of a Bohm type one assumes that all the possible measurements belong to a restricted class:
(a) we measure only positions of particles and (b) have no access to exact values of initial con-
ditions for Bohm's trajectories. However, in any computer simulation based on Bohm's equations
one relaxes the assumption (b) and yet obtains agreement with quantum predictions concerning
the results of positional measurements. Therefore a theory where (b) is relaxed, although in prin-
ciple allowing for measurements of a more general type, cannot be experimentally falsified within
the current experimental paradigm. Such generalized measurements have not been invented, or have
been invented but the information is qualified, but we cannot exclude their possibility on the basis of
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