Uncertainty, entropy, and non-Gaussianity for mixed states

Aikaterini Mandilara; Evgueni Karpov; Nicolas J. Cerf

doi:10.1117/12.854750

4 June 2010 Uncertainty, entropy, and non-Gaussianity for mixed states

Aikaterini Mandilara, Evgueni Karpov, Nicolas J. Cerf

Proceedings Volume 7727, Quantum Optics; 77270H (2010) https://doi.org/10.1117/12.854750
Event: SPIE Photonics Europe, 2010, Brussels, Belgium

Abstract

In the space of mixed states the Schrödinger-Robertson uncertainty relation holds though it can never be saturated. Two tight extensions of this relation in the space of mixed states exist; one proposed by Dodonov and Man'ko, where the lower limit on the uncertainty depends on the purity of the state, and another where the uncertainty is bounded by the von Neumann entropy of the state proposed by Bastiaans. Driven by the needs that have emerged in the field of quantum information, in a recent work we have extended the puritybounded uncertainty relation by adding an additional parameter characterizing the state, namely its degree of non-Gaussianity. In this work we alternatively present a extension of the entropy-bounded uncertainty relation. The common points and differences between the two extensions of the uncertainty relation help us to draw more general conclusions concerning the bounds on the non-Gaussianity of mixed states.

Citation Download Citation

Aikaterini Mandilara, Evgueni Karpov, and Nicolas J. Cerf "Uncertainty, entropy, and non-Gaussianity for mixed states", Proc. SPIE 7727, Quantum Optics, 77270H (4 June 2010); https://doi.org/10.1117/12.854750

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