Monogamy Inequality and Residual Entanglement of Three Qubits under Decoherence

TL;DR

This paper analyzes how three-qubit entanglement, quantified via monogamy inequality and residual entanglement, behaves under decoherence channels like phase and amplitude damping, revealing limitations of residual negativity as an entanglement measure.

Contribution

It provides an analytical expression for the convex roof of squared concurrence for rank 2 states and studies entanglement dynamics under decoherence using monogamy inequalities.

Findings

Bipartite entanglement shows similar behavior across qubits.

Residual negativity can increase under local decoherence, questioning its validity as an entanglement measure.

Residual entanglement via negativity is not reliable for mixed states.

Abstract

Exploring an analytical expression for the convex roof of the pure state squared concurrence for rank 2 mixed states the entanglement of a system of three particles under decoherence is studied, using the monogamy inequality for mixed states and the residual entanglement obtained from it. The monogamy inequality is investigated both for the concurrence and the negativity in the case of local independent phase damping channel acting on generalized GHZ states of three particles and the local independent amplitude damping channel acting on generalized W state of three particles. It is shown that the bipartite entanglement between one qubit and the rest has a qualitative similar behavior to the entanglement between individual qubits, and that the residual entanglement in terms of the negativity cannot be a good entanglement measure for mixed states, since it can increase under local decoherence.