Fabrizio Logiurato, Augusto Smerzi
The probabilistic rule that links the formalism of Quantum Mechanics (QM) to
the real world was stated by Born in 1926. Since then, there were many attempts
to derive the Born postulate as a theorem, Gleason's one being the most
prominent. The Gleason derivation, however, is generally considered as rather
intricate and its physical meaning, in particular in relation with the
noncontextuality of probability (NP), is not quite evident. More recently, we
are witnessing a revival of interest on possible demonstrations of the Born
rule, like Zurek's and Deutsch's based on the decoherence and on the theory of
decisions, respectively. Despite an ongoing debate about the presence of hidden
assumptions and circular reasonings, these have the merit of prompting more
physically oriented approaches to the problem. Here we suggest a new proof of
the Born rule based on the noncontextuality of probability. Within the theorem
we also demonstrate the continuity of probability with respect to the
amplitudes, which has been suggested to be a gap in Zurek's and Deutsch's
approaches, and we show that NP is implicitly postulated also in their
demonstrations. Finally, physical motivations are given of NP based on an
invariance principle with respect to a resolution change of measurements and
with respect to the principle of no-faster-than-light signalling.
View original:
http://arxiv.org/abs/1202.2728
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