Nonlocality threshold for entanglement under general dephasing evolutions: A case study

TL;DR

This paper derives a formula linking nonlocality and entanglement in two-qubit systems under pure dephasing, enabling the determination of conditions for maintaining nonlocal correlations in open quantum systems.

Contribution

It provides a closed-form expression for the Bell function as a function of concurrence under general dephasing, and applies it to identify initial state conditions for sustained nonlocality.

Findings

Derived a Bell function formula for dephasing systems

Identified nonlocality thresholds based on initial state purity

Showed steady entanglement can preserve nonlocal correlations

Abstract

Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal demonstration, a closed formula of the Bell function, witnessing nonlocality, as a function of the concurrence, quantifying entanglement, valid for a system of two noninteracting qubits initially prepared in extended Werner-like states undergoing any local pure-dephasing evolution. This formula allows for finding nonlocality thresholds for the concurrence depending only on the purity of the initial state. We then utilize these thresholds in a paradigmatic system where the two qubits are locally affected by a quantum environment with an Ohmic class spectrum. We show that steady entanglement can be achieved and provide the lower bound of initial state purity such that this stationary entanglement is above the nonlocality threshold thus guaranteeing the maintenance of nonlocal correlations.