Time-invariant entanglement and sudden death of nonlocality for multipartite systems under collective dephasing

TL;DR

This paper explores how multipartite quantum systems maintain constant entanglement over time despite collective dephasing, while their nonlocality can diminish, revealing complex dynamics in quantum coherence and correlations.

Contribution

It demonstrates the existence of time-invariant genuine entanglement in four-qubit systems and analyzes the differing behaviors of entanglement and nonlocality under collective dephasing.

Findings

Time-invariant entanglement exists for four-qubit states.

Nonlocality can decay even when entanglement remains constant.

No evidence of time-invariant entanglement for three-qubit states.

Abstract

We investigate the dynamics of entanglement and nonlocality for multipartite quantum systems under collective dephasing. Using an exact and computable measure for genuine entanglement, we demonstrate the possibility of a non trivial phenomenon of time-invariant entanglement for multipartite quantum systems. We find that for four qubits, there exist quantum states, which are changing continously nevertheless their genuine entanglement remains constant. Based on our numerical results, we conjecture that there is no evidence of time-invariant entanglement for quantum states of three qubits. We point out that quantum states exhibiting time-invariant entanglement must live in both decoherence free subspace and in the subspaces orthogonal to it. The previous studies on this feature for two qubits can be recovered from our studies as a special case. We also study the nonlocality of quantum states under collective dephasing. We find that although genuine entanglement of quantum states may not change, however their nonlocality changes. We discuss the possibility of finite time end of genuine nonlocality.