Unified Monogamy Relations of Multipartite Entanglement

Awais Khan,Junaid Ur Rehman,Hyundong Shin,Kehao Wang

doi:10.1038/s41598-019-52817-y

Awais Khan, Junaid Ur Rehman + Show 2 more

Open Access

https://doi.org/10.1038/s41598-019-52817-y

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Abstract

Unified-(q, s) entanglement ({{mathscr{U}}}_{q,s}) is a generalized bipartite entanglement measure, which encompasses Tsallis-q entanglement, Rényi-q entanglement, and entanglement of formation as its special cases. We first provide the extended (q; s) region of the generalized analytic formula of {{mathscr{U}}}_{q,s}. Then, the monogamy relation based on the squared {{mathscr{U}}}_{q,s} for arbitrary multiqubit mixed states is proved. The monogamy relation proved in this paper enables us to construct an entanglement indicator that can be utilized to identify all genuine multiqubit entangled states even the cases where three tangle of concurrence loses its efficiency. It is shown that this monogamy relation also holds true for the generalized W-class state. The αth power {{mathscr{U}}}_{q,s} based general monogamy and polygamy inequalities are established for tripartite qubit states.

Highlights

Entanglement is a vital asset in quantum information sciences that can enhance quantum technologies such as communication, cryptography and computing beyond classical limitations1
This paper proposes the idea to understand the entanglement distribution in multipartite system via the unified-(q, s) entanglement ( q,s). q,s encompasses several measures of entanglement such as concurrence, Tsallis-q entanglement (Tq -E), Rényi-q entanglement (Rq-E), and entanglement of formation (EOF), as its special cases
Unified-(q,s) entanglement is a two-parameter class of well defined bipartite entanglement measures

Summary

Introduction

Entanglement is a vital asset in quantum information sciences that can enhance quantum technologies such as communication, cryptography and computing beyond classical limitations1. They established the monogamy property for tripartite (A, B, and C) system via an entanglement measure called the concurrence5. This monogamy relation was generalized to N-qubit systems6. The dual of monogamy (polygamy) relation via the concurrence of assistance was proposed to quantify the limitation of distributing bipartite entanglement in multipartite systems21,22. Polygamy relations were established using various entanglement measures, e.g., convex-roof extended negativity13, and Tsallis-q entanglement9,16.

Results

Conclusion