Connection among entanglement, mixedness and nonlocality in a dynamical context

TL;DR

This paper explores how entanglement, mixedness, and nonlocality evolve and relate dynamically in a two-qubit system within a structured reservoir, revealing state-dependent behaviors and deriving new quantitative relations.

Contribution

It introduces a C-P-B parameter space to analyze the dynamical relations among entanglement, mixedness, and nonlocality, and derives new formulas linking these quantifiers for mixed states.

Findings

No universal closed relation among C, P, and B for all states.

For a specific initial state, the system remains maximally entangled and mixed.

A new expression relating C, P, and B for mixed states is proposed.

Abstract

We investigate the dynamical relations among entanglement, mixedness and nonlocality, quantifed by concurrence C, purity P and maximum of Bell function B, respectively, in a system of two qubits in a common structured reservoir. To this aim we introduce the C-P-B parameter space and analyze the time evolution of the point representative of the system state in such a space. The dynamical interplay among entanglement, mixedness and nonlocality strongly depends on the initial state of the system. For a two-excitation Bell state the representative point draws a multi-branch curve in the C-P-B space and we show that a closed relation among these quantifers does not hold. By extending the known relation between C and B for pure states, we give an expression among the three quantifers for mixed states. In this equation we introduce a quantity, vanishing for pure states which has not in general a closed form in terms of C, P and B. Finally we demonstrate that for an initial one-excitation Bell state a closed C-P-B relation instead exists and the system evolves remaining always a maximally entangled mixed state.