Generalised monogamy relation of convex-roof extended negativity in multi-level systems

TL;DR

This paper explores generalized monogamy inequalities of convex-roof extended negativity (CREN) in multi-level quantum systems, establishing bounds on bipartite entanglement and verifying these inequalities in specific multi-qubit and qudit states.

Contribution

It introduces generalized monogamy inequalities for CREN in multi-level systems and demonstrates their validity in various quantum states, extending previous entanglement bounds.

Findings

CREN provides bounds on bipartite entanglement in multi-level systems.

Monogamy relations hold for multi-qubit pure states.

Inequalities are satisfied for qudits with superposed W-class states.

Abstract

In this paper, we investigate the generalised monogamy inequalities of convex-roof extended negativity (CREN) in multi-level systems. The generalised monogamy inequalities provide the upper and lower bounds of bipartite entanglement, which are obtained by using CREN and the CREN of assistance (CRENOA). Furthermore, we show that the CREN of multi-qubit pure states satisfies some monogamy relations. Additionally, we test the generalised monogamy inequalities for qudits by considering the partially coherent superposition of a generalised W-class state in a vacuum and show that the generalised monogamy inequalities are satisfied in this case as well.