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AIP conference proceedings

Entanglement in Time and Temporal Communication Complexity

Samuel Taylor

Published Jan 1, 2004• 14 citations
Publisher

Abstract

From assumptions of reality and locality in time, we develop a temporal analogue of a Bell inequality. We show how the predictions of quantum mechanics violate this inequality. We investigate how multiple‐time correlations behave. Finally we introduce an application of this temporal correlation, showing how the violation of the temporal Bell’s inequality allows for a ‘better‐than‐classical’ solution to a temporal analogue of a communication complexity problem.

DOI
10.1063/1.1834435

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From assumptions of reality and locality in time, we develop a temporal analogue of a Bell inequality. We show how the predictions of quantum mechanics violate this inequality. We investigate how multiple‐time correlations behave. Finally we introduce an application of this temporal correlation, showing how the violation of the temporal Bell’s inequality allows for a ‘better‐than‐classical’ solution to a temporal analogue of a communication complexity problem.
Abstract Bell's theorem revealed that a local hidden-variable model cannot completely reproduce the quantum mechanical predictions. Bell's inequality provides an upper bound under the locality and reality assumptions that can be violated by correlated measurement statistics of quantum mechanics. Greenberger, Horne, and Zeilinger (GHZ) gave a more compelling proof of Bell's theorem without inequalities by considering perfect correlations rather than statistical correlations. In this work, we present a temporal analogue of GHZ argument that establishes Bell's theorem in time without inequalities .
Bell's theorem revealed that a local hidden-variable model cannot completely reproduce the quantum mechanical predictions. Bell's inequality provides an upper bound under the locality and reality assumptions that can be violated by correlated measurement statistics of quantum mechanics. Greenberger, Horne, and Zeilinger (GHZ) gave a more compelling proof of Bell's theorem without inequalities by considering perfect correlations rather than statistical correlations. This work presents a temporal analog of the GHZ argument that establishes Bell's theorem in time without inequalities.
Abstract This article presents a talk given at 23rd International Conference on Theoretical Physics (Ustroń, 2008). A new version of Bell's theorem is presented, with inequalities based on four assumptions: realism, locality and “free will” and “principle of rotational symmetry of physical laws”. The new Bell‐type inequalities are derived using a simple geometrical intuition. The assumptions behind Bell's theorem are discussed. A critique of overinterpretations of violations of Bell inequalities is given. Further on, a new criterion for entanglement is presented, based on simple geometrical ideas. This leads to a new class of entanglement identifiers, which is richer than entanglement witnesses. Finally a link between Bell's theorem and communication complexity problems will be shown. It covers also realizations, which do not involve entanglement (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
This chapter discusses temporal correlations, the relationship between what is happening at one point in time and what happens subsequently at another point. In certain experiments, classical mechanics predicts that certain inequalities must be absolutely satisfied, but quantum mechanics predicts that sometimes there may be possible violations. To illustrate this, the chapter discusses the classical Leggett–Garg inequality for classical bits and then show in detail how quantum mechanics predicts a violation of it. The chapter discusses the reasons for this spectacular result, which the chapter believes have everything to do with contextuality and the way humans have been conditioned to view reality in non-contextual classical terms.
Quantum correlations which violate a Bell inequality are presumed to power better-than-classical protocols for solving communication complexity problems (CCPs). How general is this statement? We show that violations of correlation-type Bell inequalities allow advantages in CCPs, when communication protocols are tailored to emulate the Bell no-signaling constraint (by not communicating measurement settings). Abandonment of this restriction on classical models allows us to disprove the main result of, inter alia, \cite{BZ02}; we show that quantum correlations obtained from these communication strategies assisted by a small quantum violation of the CGLMP Bell inequalities do not imply advantages in any CCP in the input/output scenario considered in the reference. More generally, we show that there exists quantum correlations, with nontrivial local marginal probabilities, which violate the I3322 Bell inequality, but do not enable a quantum advantange in any CCP, regardless of the communication strategy employed in the quantum protocol, for a scenario with a fixed number of inputs and outputs