dorsal/arxiv
View SchemaA Bell Inequality Analog in Quantum Measure Theory
| Authors | David Craig, Fay Dowker, Joe Henson, Seth Major, David Rideout, Rafael D. Sorkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605008 |
| URL | https://arxiv.org/abs/quant-ph/0605008 |
| DOI | 10.1088/1751-8113/40/3/010 |
| Journal | J.Phys.A40:501-523,2007 |
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.
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"abstract": "One obtains Bell\u0027s inequalities if one posits a hypothetical joint\nprobability distribution, or {\\it measure}, whose marginals yield the\nprobabilities produced by the spin measurements in question. The existence of a\njoint measure is in turn equivalent to a certain causality condition known as\n``screening off\u0027\u0027. We show that if one assumes, more generally, a joint {\\it\nquantal measure}, or ``decoherence functional\u0027\u0027, one obtains instead an\nanalogous inequality weaker by a factor of $\\sqrt{2}$. The proof of this\n``Tsirel\u0027son inequality\u0027\u0027 is geometrical and rests on the possibility of\nassociating a Hilbert space to any strongly positive quantal measure. These\nresults lead both to a {\\it question}: ``Does a joint measure follow from some\nquantal analog of `screening off\u0027?\u0027\u0027, and to the {\\it observation} that\nnon-contextual hidden variables are viable in histories-based quantum\nmechanics, even if they are excluded classically.",
"arxiv_id": "quant-ph/0605008",
"authors": [
"David Craig",
"Fay Dowker",
"Joe Henson",
"Seth Major",
"David Rideout",
"Rafael D. Sorkin"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1088/1751-8113/40/3/010",
"journal_ref": "J.Phys.A40:501-523,2007",
"title": "A Bell Inequality Analog in Quantum Measure Theory",
"url": "https://arxiv.org/abs/quant-ph/0605008"
},
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