Bound on distributed entanglement

TL;DR

This paper establishes lower bounds on the amount of entanglement that can be remotely distributed between quantum systems using joint measurements, with specific results for two-qubit and two-qutrit systems and conditions for higher dimensions.

Contribution

It introduces bounds on distributed entanglement using convex-roof negativity and negativity of assistance, extending to higher-dimensional systems under certain conditions.

Findings

The distributed entanglement is at least the product of initial entanglements in two-qubit and two-qutrit systems.

Provides sufficient conditions for generalization to higher-dimensional systems.

Quantifies the limits of entanglement distribution via joint measurements.

Abstract

Using the convex-roof extended negativity and the negativity of assistance as quantifications of bipartite entanglement, we consider the possible remotely-distributed entanglement. For two pure states $\ket{\phi}_{AB}$ and $\ket{\psi}_{CD}$ on bipartite systems $AB$ and $CD$, we first show that the possible amount of entanglement remotely distributed on the system $AC$ by joint measurement on the system $BD$ is not less than the product of two amounts of entanglement for the states $\ket{\phi}_{AB}$ and $\ket{\psi}_{CD}$ in two-qubit and two-qutrit systems. We also provide some sufficient conditions, for which the result can be generalized into higher-dimensional quantum systems.