Unifying nonclassical correlation via Tsallis α-entropy and its application in bilocal scenario

This article introduces a new variant of a family of measurement-induced nonlocality (MIN) measures using Tsallis alpha-relative entropy (T alpha E). We show that the proposed MIN measure satisfies all the axioms of a faithful measure of quantum correlation and resolves the local ancilla issue of Hilbert-Schmidt MIN. Analytically, we evaluate the MIN for an arbitrary pure state and 2 x n-dimensional mixed state. We also establish the simple relations between Tsallis MIN and the other MINs available in the literature. Extending the notion of the Tsallis entropy-based MIN, we characterize the nonbilocal correlation in a bilocal scenario and identify the closer connection between the nonlocal and nonbilocal correlation measures.

Automated summary

This article introduces a new variant of measurement-induced nonlocality measures using Tsallis alpha-relative entropy. The proposed measure satisfies the axioms of a faithful measure of quantum correlation and resolves some issues of previous methods. Analytically, the measure is evaluated for both pure and mixed states, and its relations with other measures in the literature are established. The article also extends the method to characterize nonbilocal correlation in a bilocal scenario and identifies a closer connection between nonlocal and nonbilocal correlation measures.