Local correlations of mixed two-qubit states

TL;DR

This paper investigates the local and nonlocal components of two-qubit states' measurement distributions, establishing a lower bound related to concurrence and constructing local distributions for specific mixed states.

Contribution

It introduces a lower bound on the local weight of two-qubit states based on concurrence and constructs explicit local distributions for certain mixed states.

Findings

Lower bound of local weight linked to concurrence: $p_L^{ ext{max}}= 1- ext{Concurrence}( ho)$

Constructed local distributions for two families of mixed states

Results align with the theoretical lower bound

Abstract

The quantum probability distribution arising from single-copy von Neumann measurements on an arbitrary two-qubit state is decomposed into the local and nonlocal parts, in the approach of Elitzur, Popescu and Rohrlich [A. Elitzur, S. Popescu, and D. Rohrlich, Phys. Lett. A 162, 25 (1992)]. A lower bound of the local weight is proved being connected with the concurrence of the state $p_L^{\max}= 1-\mathcal{C}(\rho)$. The local probability distributions for two families of mixed states are constructed independently, which accord with the lower bound.