Concurrence for infinite-dimensional quantum systems

TL;DR

This paper extends the entanglement measure called concurrence to infinite-dimensional quantum systems, demonstrating its properties and relating it to the PHC measure for a broader understanding of quantum entanglement.

Contribution

It introduces a definition of concurrence for infinite-dimensional systems and shows its equivalence with the PHC measure, expanding entanglement quantification methods.

Findings

Concurrence is continuous in infinite-dimensional systems.

Concurrence does not increase under LOCC.

PHC measure coincides with concurrence.

Abstract

Concurrence is an important entanglement measure for states in finite-dimensional quantum systems that was explored intensively in the last decade. In this paper, we extend the concept of concurrence to infinite-dimensional bipartite systems and show that it is continuous and does not increase under local operation and classical communication (LOCC). Moreover, based on the partial Hermitian conjugate (PHC) criterion proposed in [Chin. Phys. Lett. \textbf{26}, 060305(2009); Chin. Sci. Bull. \textbf{56}(9), 840--846(2011)], we introduce a concept of the PHC measure and show that it coincides with the concurrence, which provides another perspective on the concurrence.