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

• URL: http://arxiv.org/abs/2105.14938v1
• Date: Mon, 31 May 2021 13:05:08 GMT
• Title: On overall measure of non-classicality of $N$-level quantum system and its universality in the large $N$ limit
• Authors: Vahagn Abgaryan, Arsen Khvedelidze, Ilya Rogojin
• Abstract summary: We introduce a global measure of non-classicality of the state space of $N$-level quantum systems. We prove a proposition claiming its exact value in the limit of $Nto infty$
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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