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arXiv · 1005.1665

Directly estimating non-classicality

A. Mari·K. Kieling·B. Melholt Nielsen·E. S. Polzik·J. Eisert
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Abstract

We establish a method of directly measuring and estimating non-classicality - operationally defined in terms of the distinguishability of a given state from one with a positive Wigner function. It allows to certify non-classicality, based on possibly much fewer measurement settings than necessary for obtaining complete tomographic knowledge, and is at the same time equipped with a full certificate. We find that even from measuring two conjugate variables alone, one may infer the non-classicality of quantum mechanical modes. This method also provides a practical tool to eventually certify such features in mechanical degrees of freedom in opto-mechanics. The proof of the result is based on Bochner's theorem characterizing classical and quantum characteristic functions and on semi-definite programming. In this joint theoretical-experimental work we present data from experimental optical Fock state preparation, demonstrating the functioning of the approach.

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A. Mari, K. Kieling, B. Melholt Nielsen, E. S. Polzik, J. Eisert. 2010-05-26. Directly estimating non-classicality. https://doi.org/10.1103/physrevlett.106.010403

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