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Physical Review A

Nonclassicality tests by classical bounds on the statistics of multiple outcomes

Alfredo Luis

Published Aug 18, 2010• 3 citations
Publisher

Abstract

We derive simple practical tests revealing the quantum nature of states by the violation of classical upper bounds on the statistics of multiple outcomes of an observable. These criteria can be expressed in terms of the Kullback-Leibler divergence (or relative entropy). Nonclassicality tests for multiple outcomes can be satisfied by states that do not fulfill the corresponding single-outcome criteria.

DOI
10.1103/physreva.82.024101

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We derive simple practical tests revealing the quantum nature of states by the violation of classical upper bounds on the statistics of multiple outcomes of an observable. These criteria can be expressed in terms of the Kullback-Leibler divergence (or relative entropy). Nonclassicality tests for multiple outcomes can be satisfied by states that do not fulfill the corresponding single-outcome criteria.
We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum, and definite conclusions are obtained without evaluation of moments or any other more sophisticated procedures. These nonclassical tests are independent of other typical quantum signatures such as sub-Poissonian statistics, quadrature squeezing, or oscillatory statistics. This approach can be equally well applied to very diverse situations such as single- and two-mode fields, observables with continuous and discrete spectra, finite- and infinite-dimensional systems, and ideal and noisy measurements.
We derive simple practical procedures revealing the quantum behavior of angular momentum variables by the violation of classical upper bounds on the statistics. Data analysis is minimum and definite conclusions are obtained without evaluation of moments, or any other more sophisticated procedures. These nonclassical tests are very general and independent of other typical quantum signatures of nonclassical behavior such as sub-Poissonian statistics, squeezing, or oscillatory statistics, being insensitive to the nonclassical behavior displayed by other variables.
Nonclassicality cannot be a single-observable property, since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior of light states from the joint statistics arising in the practical measurement of multiple observables. Beside embracing previous approaches, this protocol can disclose nonclassical features for standard examples of classical-like behavior, such as SU(2) and Glauber coherent states. When combined with other criteria, this would imply that every light state is nonclassical.
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