Continuity equations for entanglement

TL;DR

This paper introduces a continuity equation framework for entanglement in continuous variable quantum systems, proposing a new measure of entanglement complexity based on the dynamics of a complex purity density.

Contribution

It develops a novel continuity equation approach for entanglement, linking global and local quantum correlations, and suggests a new complexity measure for entanglement dynamics.

Findings

Introduces a complex purity density and current for pure states.

Establishes a continuity equation-based entanglement subdynamics.

Proposes dimensionality of entanglement subdynamics as a complexity measure.

Abstract

We introduce a complex purity density and its associated current for pure states of continuous variable systems. The scheme is constructed by analogy with the notions of probability density and probability current. Taking advantage of the formal continuity equations obtained this way we can introduce an entanglement subdynamics. We suggest the use of the dimensionality of this subdynamics as a potential measure of the complexity of entanglement. The scheme also provides insights into the relation between the global and local aspects of quantum correlations.