|
| related topics |
| {vol, operators, histories} |
| {bell, inequality, local} |
| {theory, mechanics, state} |
| {let, theorem, proof} |
| {particle, mechanics, theory} |
| {observables, space, algebra} |
| {measurement, state, measurements} |
| {time, systems, information} |
| {field, particle, equation} |
| {photon, photons, single} |
| {cavity, atom, atoms} |
| {level, atom, field} |
|
A Bell Inequality Analog in Quantum Measure Theory
David Craig, Fay Dowker, Joe Henson, Seth Major, David Rideout, Rafael D. Sorkin
abstract: 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0605008
- categories:
- quant-ph gr-qc
- comments:
- 38 pages, TeX. Several changes and added comments to bring out the
meaning more clearly. Minor rewording and extra acknowledgements, now closer
to published version
- doi:
- 10.1088/1751-8113/40/3/010
- arxiv_id:
- quant-ph/0605008
- journal_ref:
- J.Phys.A40:501-523,2007
- created:
- 2006-04-30
- updated:
- 2006-12-11
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