Evolution equation of entanglement for multi-qubit systems

TL;DR

This paper derives an evolution equation for entanglement in multi-qubit systems under noise, enabling analysis of entanglement dynamics in complex quantum states affected by various noise channels.

Contribution

It introduces a new evolution equation for a lower bound of multi-qubit concurrence, advancing understanding of entanglement dynamics under noise.

Findings

Entanglement evolution can be described by the derived equation.

Entanglement decay varies with different noise channels.

The method applies to mixed three-qubit states involving GHZ and W states.

Abstract

We discuss entanglement evolution of a multi-qubit system when one of its qubits is subjected to a general noisy channel. For such a system, an evolution equation of entanglement for a lower bound for multi-qubit concurrence is derived. Using this evolution equation, the entanglement dynamics of an initially mixed three-qubit state composed of a GHZ and a W state is analyzed if one of the qubits is affected by a phase, an amplitude or a generalized amplitude damping channel.