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arXiv · 2105.14938

On overall measure of non-classicality of $N$-level quantum system and its universality in the large $N$ limit

Vahagn Abgaryan·Arsen Khvedelidze·Ilya Rogojin
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Abstract

In this report we are aiming at introducing a global measure of non-classicality of the state space of $N$-level quantum systems and estimating it in the limit of large $N$. For this purpose we employ the Wigner function negativity as a non-classicality criteria. Thus, the specific volume of the support of negative values of Wigner function is treated as a measure of non-classicality of an individual state. Assuming that the states of an $N$-level quantum system are distributed by Hilbert-Schmidt measure (Hilbert-Schmidt ensemble), we define the global measure as the average non-classicality of the individual states over the Hilbert-Schmidt ensemble. We present the numerical estimate of this quantity as a result of random generation of states, and prove a proposition claiming its exact value in the limit of $N\to \infty$

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Vahagn Abgaryan, Arsen Khvedelidze, Ilya Rogojin. 2021-05-31. On overall measure of non-classicality of $N$-level quantum system and its universality in the large $N$ limit. https://doi.org/10.1007/978-3-030-66471-8_20

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