Characterizing nonclassical correlations of tensorizing states in a bilocal scenario

TL;DR

This paper investigates whether tensorizing states can exhibit quantum advantages by introducing a fidelity-based nonbilocal measure and analyzing its properties and bounds, revealing insights into nonlocal effects in quantum states.

Contribution

It proposes a new fidelity-based nonbilocal measure to quantify nonlocal effects in tensorizing states and analytically evaluates this measure for arbitrary pure states.

Findings

The nonbilocal measure aligns with measurement-induced nonlocality properties.

Analytical bounds are derived based on eigenvalues of the correlation matrix.

Computed nonbilocality for several well-known quantum states.

Abstract

In the present paper, we attempt to address the question of "can tensorizing states have quantum advantages?". To answer this question, we exploit the notion of measurement-induced nonlocality (MIN) and advocate a fidelity based nonbilocal measure to capture the nonlocal effects of tensorizing states due to locally invariant von Neumann projective measurements. We show that the properties of the fidelity based nonbilocal measure are retrieved from that of MIN. Analytically, we evaluate the nonbilocal measure for any arbitrary pure state. The upper bounds of the nonbilocal measure based on fidelity are also obtained in terms of eigenvalues of correlation matrix. As an illustration, we have computed the nonbilocality for some popular input states.