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Directly estimating non-classicality · Around

2010

Directly estimating non-classicality

Mari, A., Kieling, K., Nielsen, B. Melholt et al.

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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.

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Since the error follows a Gaussian distribution, the probability P out P_{\text{out}} that the actual value of the characteristic function lies outside the error bar is never zero but it is exponentially suppressed for increasing n n . E.g., for n = 3 n=3 one has P out < 2.7 × 10 − 3 P_{\text{out}}<2.7\times 10^{-3} , for n = 5 n=5 one has P out < 6 × 10 − 7 P_{\text{out}}<6\times 10^{-7} , etc

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D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, arxiv:0909.3304; A. Shabani, R. L. Kosut and H. Rabitz, arXiv:0910.5498

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S. T. Flammia, D. Gross, S. D. Bartlett, and R. Somma, arXiv:1002.3839; M. Cramer and M. B. Plenio, arXiv:1002.3780

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