Optimal two-qubit states for quantum teleportation vis-\`a-vis state properties

TL;DR

This paper characterizes two-qubit states that optimize quantum teleportation fidelity for specific state properties, identifying conditions for maximal fidelity and zero fidelity deviation.

Contribution

It provides a complete characterization of optimal states for given linear entropy, Bell-CHSH violation, and concurrence, revealing their relationships.

Findings

Optimal states achieve maximal fidelity for given linear entropy and Bell-CHSH violation.

For a fixed concurrence, optimal states are a subset of the maximal fidelity states.

Optimal states exhibit zero fidelity deviation, ensuring consistent teleportation performance.

Abstract

Quantum teleportation with a two-qubit state can be suitably characterized in terms of maximal fidelity and fidelity deviation, where the former is the maximal value of the average fidelity achievable within the standard protocol and local unitary operations and the latter is the standard deviation of fidelity over all input states. In this paper, we consider the problem of characterizing two-qubit states that are optimal for quantum teleportation for a given value of some state property. The optimal states are defined as those states that, for a given value of the state property under consideration, achieve the largest maximal fidelity and also exhibit zero fidelity deviation. We provide a complete characterization of optimal states for a given linear entropy, maximum mean value of the Bell-CHSH observable, and concurrence, respectively. We find that for a given linear entropy or Bell-CHSH violation, the largest maximal fidelity states are optimal, but for a given concurrence, the optimal states form a strict subset of the largest maximal fidelity states.