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Acta Physica Polonica A

Violation of Bell--CHSH--CH Inequalities by Superposition of Two Coherent States (π/2 Out of Phase)

Devendra Kumar Mishra

Published Jan 1, 2013• 3 citations
Publisher

Abstract

We study the tests of the BellCHSH & CH inequalities by superposition of two coherent states (π/2 out of phase), a class of non-Gaussian state, using photon parity and on/o measurements.Large violations of the Bell--type inequalities have been observed theoretically conrming the interpretation and validity of quantum mechanics against the local-realistic theories.

DOI
10.12693/aphyspola.123.21

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We study the tests of the BellCHSH & CH inequalities by superposition of two coherent states (π/2 out of phase), a class of non-Gaussian state, using photon parity and on/o measurements.Large violations of the Bell--type inequalities have been observed theoretically conrming the interpretation and validity of quantum mechanics against the local-realistic theories.
Quantum nonlocality can be tested in experiments via the violation of the Bell inequality. We propose novel methods of the rearrangement and linear inequality to prove all the known Bell-CH inequalities of Imn22Imn22Imn22-type (m,n≤5m,n\le5m,n≤5). We also derive a set of new Bell-CH inequalities by using these methods which should be violated in quantum entangled states.
Bell-type inequalities and violations thereof reveal the fundamental differences between standard probability theory and its quantum counterpart. In the course of previous investigations ultimate bounds on quantum mechanical violations have been found. For example, Tsirelson's bound constitutes a global upper limit for quantum violations of the Clauser-Horne-Shimony-Holt (CHSH) and the Clauser-Horne (CH) inequalities. Here we investigate a method for calculating the precise quantum bounds on arbitrary Bell-type inequalities by solving the eigenvalue problem for the operator associated with each Bell-type inequality. Thereby, we use the min-max principle to calculate the norm of these self-adjoint operators from the maximal eigenvalue yielding the upper bound for a particular set of measurement parameters. The eigenvectors corresponding to the maximal eigenvalues provide the quantum state for which a Bell-type inequality is maximally violated.
One of the essential features of quantum theory is the noncommutativity of observables. Moreover, under the non-contextual realistic interpretations of quantum theory, all quantum observables must commute {[J. D. Malley, Phys. Rev. A {\\bf 69}, 022118 (2004)]}. Experimental realizations of violations of Bell inequality say the noncommutativity of observables in an entangled state. Here we show that commutativity can be tested experimentally using uncorrelated states, with no dependence on the algebraic structure of the observables under study. The test is derived from the bounds of an inequality valid for all commuting observables. For nnn spin-1/2 systems we show that an nnn-partite uncorrelated state violates the inequality by an amount that grows exponentially with nnn.