This article introduces a new variant of a family of measurement-induced nonlocality (MIN) measures using Tsallis α−relative entropy (TαE). 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×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.
Measurement-induced nonlocality (MIN) was proposed for measure the maximum global effect caused by locally invariant measurements. Similarly, the Measurement-induced nonbilocal correlation is a generalization of MIN can be used to measure the maximal global influence caused by the local measurement in the bilocal scenario. In this paper, we propose a new nonbilocal correlation measure based on the Wigner-Yanase skew information. The relationship between the MIN based on Wigner-Yanase skew information and our measure is discussed. We present an analytical expression of our measure for pure input states and also provide upper bounds for input general mixed states.
The nonlocality revealed in a multiparty multisource network Bell experiment is conceptually different than the standard multiparty Bell nonlocality involving a single common source. Here, by introducing variants of asymmetric bilocal as well as trilocal network scenarios, we go beyond the typical bilocal network scenario where both the edge parties have an equal number of measurement settings. We first introduce an asymmetric bilocal network where one of the edge parties (say, Alice) receives ${2}^{n\ensuremath{-}1}$ inputs and the other edge party (say, Charlie) receives
n inputs. We derive two variants of asymmetric bilocality inequalities and demonstrate their optimal quantum violations. Further, we explore two types of asymmetric trilocal scenarios: (i) when two edge parties receive ${2}^{n\ensuremath{-}1}$ inputs each and the other edge party receives
n inputs, and (ii) when one edge party receives ${2}^{n\ensuremath{-}1}$ inputs and the other two edge parties have
n inputs each. We use an elegant sum-of-squares technique that enables us to evaluate the quantum optimal values of the proposed network inequalities without assuming the dimension of the systems for both the asymmetric bilocal as well as the trilocal scenarios. Further, we demonstrate the robustness of the quantum violations of the proposed inequalities in the presence of white noise.