Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity

TL;DR

This paper introduces convex-roof extended negativity (CREN) as a new measure to study entanglement monogamy in multipartite higher-dimensional quantum systems, showing it overcomes limitations of previous measures like concurrence.

Contribution

It demonstrates that CREN can replace concurrence in monogamy relations, extending their validity to higher-dimensional systems without known counterexamples.

Findings

CREN-based monogamy relations are consistent with known results.

CREN extends monogamy relations to qudits where concurrence fails.

CREN shows no counterexamples in tested qudit states.

Abstract

We propose replacing concurrence by convex-roof extended negativity (CREN) for studying monogamy of entanglement (MoE). We show that all proven MoE relations using concurrence can be rephrased in terms of CREN. Furthermore we show that higher-dimensional (qudit) extensions of MoE in terms of CREN are not disproven by any of the counterexamples used to disprove qudit extensions of MoE in terms of concurrence. We further test the CREN version of MoE for qudits by considering fully or partially coherent mixtures of a qudit W-class state with the vacuum and show that the CREN version of MoE for qudits is satisfied in this case as well. The CREN version of MoE for qudits is thus a strong conjecture with no obvious counterexamples.