A Bell Inequality Analog in Quantum Measure Theory

Details A Bell Inequality Analog in Quantum Measure Theory A Bell Inequality Analog in Quantum Measure Theory

2006-04-30

arxiv.org/abs/quant-ph/0605008v3

J.Phys.A40:501-523,2007

Physics

Quantum Physics

38 pages, TeX. Several changes and added comments to bring out the meaning more clearly. Minor rewording and extra acknowledge

Scientific paper

10.1088/1751-8113/40/3/010

One obtains Bell's inequalities if one posits a hypothetical joint probability distribution, or {\it measure}, whose marginals yield the probabilities produced by the spin measurements in question. The existence of a joint measure is in turn equivalent to a certain causality condition known as ``screening off''. We show that if one assumes, more generally, a joint {\it quantal measure}, or ``decoherence functional'', one obtains instead an analogous inequality weaker by a factor of $\sqrt{2}$. The proof of this ``Tsirel'son inequality'' is geometrical and rests on the possibility of associating a Hilbert space to any strongly positive quantal measure. These results lead both to a {\it question}: ``Does a joint measure follow from some quantal analog of `screening off'?'', and to the {\it observation} that non-contextual hidden variables are viable in histories-based quantum mechanics, even if they are excluded classically.

Affiliated with

Also associated with

No associations

Rating

A Bell Inequality Analog in Quantum Measure Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Bell Inequality Analog in Quantum Measure Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Bell Inequality Analog in Quantum Measure Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-47434