dorsal/arxiv
View SchemaSignal-Locality and Subquantum Information in Deterministic Hidden-Variables Theories
| Authors | Antony Valentini |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112151 |
| URL | https://arxiv.org/abs/quant-ph/0112151 |
| Journal | 'Non-Locality and Modality', eds. T. Placek and J. Butterfield (Kluwer, 2002), pp. 81-103 |
Abstract
It is proven that any deterministic hidden-variables theory, that reproduces quantum theory for a 'quantum equilibrium' distribution of hidden variables, must predict the existence of instantaneous signals at the statistical level for hypothetical 'nonequilibrium ensembles'. This 'signal-locality theorem' generalises yet another feature of the pilot-wave theory of de Broglie and Bohm, for which it is already known that signal-locality is true only in equilibrium. Assuming certain symmetries, lower bounds are derived on the 'degree of nonlocality' of the singlet state, defined as the (equilibrium) fraction of outcomes at one wing of an EPR-experiment that change in response to a shift in the distant angular setting. It is shown by explicit calculation that these bounds are satisfied by pilot-wave theory. The degree of nonlocality is interpreted as the average number of bits of 'subquantum information' transmitted superluminally, for an equilibrium ensemble. It is proposed that this quantity might provide a novel measure of the entanglement of a quantum state, and that the field of quantum information would benefit from a more explicit hidden-variables approach. It is argued that the signal-locality theorem supports the hypothesis, made elsewhere, that in the remote past the universe relaxed to a state of statistical equilibrium at the hidden-variable level, a state in which nonlocality happens to be masked by quantum noise.
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"abstract": "It is proven that any deterministic hidden-variables theory, that reproduces\nquantum theory for a \u0027quantum equilibrium\u0027 distribution of hidden variables,\nmust predict the existence of instantaneous signals at the statistical level\nfor hypothetical \u0027nonequilibrium ensembles\u0027. This \u0027signal-locality theorem\u0027\ngeneralises yet another feature of the pilot-wave theory of de Broglie and\nBohm, for which it is already known that signal-locality is true only in\nequilibrium. Assuming certain symmetries, lower bounds are derived on the\n\u0027degree of nonlocality\u0027 of the singlet state, defined as the (equilibrium)\nfraction of outcomes at one wing of an EPR-experiment that change in response\nto a shift in the distant angular setting. It is shown by explicit calculation\nthat these bounds are satisfied by pilot-wave theory. The degree of nonlocality\nis interpreted as the average number of bits of \u0027subquantum information\u0027\ntransmitted superluminally, for an equilibrium ensemble. It is proposed that\nthis quantity might provide a novel measure of the entanglement of a quantum\nstate, and that the field of quantum information would benefit from a more\nexplicit hidden-variables approach. It is argued that the signal-locality\ntheorem supports the hypothesis, made elsewhere, that in the remote past the\nuniverse relaxed to a state of statistical equilibrium at the hidden-variable\nlevel, a state in which nonlocality happens to be masked by quantum noise.",
"arxiv_id": "quant-ph/0112151",
"authors": [
"Antony Valentini"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th"
],
"journal_ref": "\u0027Non-Locality and Modality\u0027, eds. T. Placek and J. Butterfield\n (Kluwer, 2002), pp. 81-103",
"title": "Signal-Locality and Subquantum Information in Deterministic Hidden-Variables Theories",
"url": "https://arxiv.org/abs/quant-ph/0112151"
},
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