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arXiv · 1909.09433

A geometric measure of non-classicality

Paulina Marian·Tudor A. Marian
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Abstract

This paper aims to stress the role of the Cahill-Glauber quasi-probability densities in defining, detecting, and quantifying the non-classicality of field states in quantum optics. The distance between a given pure state and the set of all pure classical states is called here a geometric degree of non-classicality. As such, we investigate non-classicality of a pure single-mode state of the radiation field by using the coherent states as a reference set of pure classical states. It turns out that any such distance is expressed in terms of the maximal value of the Husimi $Q$ function. As an insightful application we consider the de-Gaussification process produced when preparing a quantum state by adding $p$ photons to a pure Gaussian one. For a coherent-state input, we get an analytic degree of non-classicality which compares interestingly with the previously evaluated entanglement potential. Then we show that addition of a single photon to a squeezed vacuum state causes a considerable enhancement of non-classicality, especially at weak and moderate squeezing of the original state. By contrast, addition of further photons is less effective.

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Paulina Marian, Tudor A. Marian. 2019-12-10. A geometric measure of non-classicality. https://doi.org/10.1088/1402-4896%2Fab631f

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