Entanglement of a mixed state of two qubit system

TL;DR

This paper proposes an alternative way to quantify entanglement in mixed two-qubit states by averaging pure state concurrences over all possible realizations, addressing the challenge posed by environment-induced state mixing.

Contribution

It introduces a new definition of concurrence for mixed states based on averaging pure state concurrences over quantum ensembles.

Findings

New formula for mixed state concurrence as an average of pure state concurrences.

Provides a method to quantify entanglement in mixed states affected by environment.

Addresses the problem of defining entanglement for mixed quantum states.

Abstract

Interaction with environment may lead to the transition of quantum system from pure state to the mixed one. In this case, the problem of definition of entanglement may arise. In particular, quantitative measure of entanglement concurrence is introduced differently for pure and mixed states. To solve this problem, alternative definition of concurrence of mixed states is introduced in present work. In particular, concurrence of mixed states is determined as an average of pure states concurrences. Averaging is carried out over the quantum ensemble, corresponding to all possible realization of random variable.