Quantum Entanglement and Order Parameter in a Paired Finite Fermi System

TL;DR

This paper explores the relationship between quantum entanglement and the order parameter in finite Fermi systems, proposing new measures to distinguish superconducting states using entanglement concepts.

Contribution

It introduces a novel approach linking entanglement measures with the order parameter in finite superconducting systems, including a generalization of spin flip transformation.

Findings

Concurrence is effective for infinite systems but not for finite ones.

Radial operator expectation value can identify pairing entanglement.

Proposes a generalized time reversal for entanglement measurement.

Abstract

We study the pairing correlations in a finite Fermi system from quantum entanglement point of view. We investigate the relation between the order parameter, which has been introduced recently to describe both finite and infinite superconductors, and the concurrence. For a proper definition of the concurrence, we argue that a possible generalization of spin flip transformation is time reversal operation. While for a system with indefinite number of particles concurrence is a good measure of entanglement, for a finite system it does not distinguish between normal and superconducting states. We propose that the expectation value of the radial operator for the total pseudospin can be used to identify entanglement of pairing.