Monogamy of entanglement and teleportation capability

TL;DR

This paper investigates the monogamy properties of entanglement and teleportation capabilities in quantum states, showing that certain monogamy inequalities hold for pure states but generally fail for mixed states.

Contribution

It introduces monogamy inequalities based on the fully entangled fraction and teleportation fidelity, highlighting their limitations for mixed states.

Findings

Monogamy inequalities hold for pure states.

Monogamy inequalities do not generally hold for mixed states.

The inequalities are valid in the context of $n$-qubit pure states.

Abstract

The monogamy inequality in terms of the concurrence, called the Coffman-Kundu-Wootters inequality [Phys. Rev. A {\bf 61}, 052306 (2000)], and its generalization [T.J. Osborne and F. Verstraete, Phys. Rev. Lett. {\bf 96}, 220503 (2006)] hold on general $n$-qubit states including mixed ones. In this paper, we consider the monogamy inequalities in terms of the fully entangled fraction and the teleportation fidelity. We show that the monogamy inequalities do not hold on general mixed states, while the inequalities hold on $n$-qubit pure states.