QUANTUM COMPUTATIONPRESS




David A. Meyer,
``Finite precision measurement nullifies the Kochen-Specker theorem'',
Physical Review Letters 83 (1999) 3751-3754,
quant-ph/9905080.

Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S2, can be colored (as indicated by the figure on the left) so that the contradiction with hidden variable theories provided by Kochen-Specker constructions does not obtain. Thus, in contrast to violation of the Bell inequalities, no quantum-over-classical advantage for information processing can be derived from the Kochen-Specker theorem alone.

PlainTeX (7 pages): PostScript (111K), PDF (114K).

Adrian Kent has generalized this result to arbitrary finite dimensional real or complex Hilbert spaces in ``Non-contextual hidden variables and physical measurements'', quant-ph/9906006. He and Rob Clifton have also developed a hidden variables model based on these ideas: ``Simulating quantum mechanics by non-contextual hidden variables'', quant-ph/9908031. In response, Jim Ax and Simon Kochen have tried to formalize what should be meant by a finite precision Kochen-Specker theorem. Adán Cabello has also commented in quant-ph/9911024 on the interpretation of these results. David Mermin argues that continuity of probabilities weighs against nullification in quant-ph/9912081. Marcus Appleby expands on part of Mermin's discussion in quant-ph/0005010.


Last modified: 3 may 00.