Generation of Maximally Entangled States by Lyapunov Control Based on Entanglement Measure

TL;DR

This paper presents a novel Lyapunov control method based on entanglement measures, enabling the generation of maximally entangled states without prior knowledge of their structure, applicable to various quantum systems.

Contribution

It introduces an entanglement measure-based Lyapunov control approach that can produce any MES regardless of its structure, overcoming limitations of previous state transfer methods.

Findings

Successfully generates Bell states and equivalents in bipartite pure states.

Extends to bipartite mixed states and multipartite systems.

Control scheme is unaffected by the number of subsystems.

Abstract

Maximally entangled states (MES) are highly valued in quantum information processing. In quantum control, the creation of MES is typically treated as a state transfer problem with a predefined MES as the target. However, this approach is limited by the requirement to predetermine the MES structure. This paper introduces an improved quantum Lyapunov control approach that relies on the quantum entanglement measure to construct the Lyapunov function, instead of using the distance between quantum states. This strategy enables the preparation of any MES, regardless of whether its structure is known beforehand, using a single control scheme. The proposed entanglement control technique is unaffected by the number of entangled subsystems since it targets the entanglement measure as a scalar. Initially applied to bipartite pure states, this method demonstrates its capability to generate Bell states and their equivalents. Subsequent applications to bipartite mixed states and multipartite systems illustrate that the technique can produce MES with unspecified structures.