On Overall Measure of Non-classicality of N-level Quantum System and Its Universality in the Large N Limit

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→ ∞. © 2020, Springer Nature Switzerland AG.