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

Tian Tian,Yu Luo,Yongming Li

doi:10.1038/srep36700

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.

Highlights

In this paper, we investigate the generalised monogamy inequalities of convex-roof extended negativity (CREN) in multi-level systems
The property of monogamy property has been considered in many areas of physics: it can be used to extract an estimate of the quantity of information about a secret key captured by an eavesdropper in quantum cryptography[10,11], as well as the frustration effects observed in condensed matter physics[12,13] and even black-hole physics[14,15]
We test the generalised monogamy inequalities for qudits by considering the partially coherent superposition of a generalised W-class state in a vacuum, and we show that the generalised monogamy inequalities are satisfied in this case as well

Summary

Results

This paper is organised as follows: in the first subsection, we recall some basic concepts of concurrence and negativity. Where the maximum is taken over all possible pure state decompositions {pi, |ψi〉AB} of ρAB Another well-known quantification of bipartite entanglement is negativity. Where the minimum is taken over all possible pure state decompositions {pi, |ψi〉AB} of ρAB. CREN is equivalent to concurrence for any pure state with Schmidt rank-217, and it follows that for any two-qubit mixed state ρAB =∑ipi|ψi〉〈ψi|: Nc (ρAB) = min ∑pi N( ψi AB ) = min ∑pi C( ψi AB ) = C(ρAB). The dual inequality in terms of COA is as follows33: 2(ρA BC) ≤ a2(ρAB) + a2(ρAC)

For any pure state ψ the CKW inequality is

We now explore theorems

Conclusions

Additional Information