Bound on remote preparation of entanglement from isotropic states

TL;DR

This paper analyzes the limits of remotely preparing entanglement from isotropic states in higher-dimensional systems, showing optimality conditions for generalized Bell measurements and proposing improved measurements for low-fidelity states.

Contribution

It provides a quantitative bound on remote entanglement preparation from isotropic states and identifies measurement strategies that optimize this process based on state fidelity.

Findings

Generalized Bell-measurements are optimal for high-fidelity isotropic states.

A new measurement surpasses Bell-measurements for low-fidelity states.

Derived bounds depend on the fidelity and system dimension.

Abstract

Using the negativity as an entanglement measure, we investigate the possible amount of remotely prepared entanglement. For two identical isotropic states on two-qudit systems 12 and 34, we calculate the average amount of entanglement remotely distributed on the system 13 by joint measurement on the system 24, and show that the remote preparation of entanglement by the generalized Bell-measurement is optimal among rank-one measurements if the isotropic states have a certain fidelity with a maximally entangled state in higher dimensional quantum systems, or if the fidelity of the isotropic states is greater than a certain value depending on the dimension. In addition, we construct a measurement better than the generalized Bell-measurement with respect to the remote preparation of entanglement when the isotropic states have small fidelity.