Concurrence and a proper monogamy inequality for arbitrary quantum states

TL;DR

This paper derives a new analytical lower bound for concurrence in bipartite quantum states and proposes a proper entanglement monogamy inequality applicable to arbitrary quantum states, addressing limitations in higher dimensions.

Contribution

It introduces a tight lower bound for concurrence and a revised entanglement monogamy inequality valid for all quantum states, including higher-dimensional systems.

Findings

New lower bound for concurrence in bipartite states

The bound is tight for some mixed states

A proper monogamy inequality for arbitrary quantum states

Abstract

We obtain an analytical lower bound of entanglement quantified by concurrence for arbitrary bipartite quantum states. It is shown that our bound is tight for some mixed states and is complementary to the previous known lower bounds. On the other hand, it is known that the entanglement monogamy inequality proposed by Coffman, Kundu, and Wootters is in general not true for higher dimensional quantum states. Inducing from the new lower bound of concurrence, we find a proper form of entanglement monogamy inequality for arbitrary quantum states.