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International Journal of Quantum Information

Product-form monogamy relations of entanglement in multiqubit systems

Jiabin Zhang, Tao Li, Zhi‐Xi Wang

Published Aug 1, 2021• 2 citations
Publisher

Abstract

Monogamy relations of entanglement play an important role in quantum systems, however, most of them are given in summation form. In this paper, we investigate the product-form monogamy relations of multipartite entanglement in terms of the [Formula: see text]th power of concurrence and negativity. Compared with the existing monogamy relations, the product-form monogamy relations of multi-body quantum entanglement have a stricter lower bound.

DOI
10.1142/s0219749921500222

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Monogamy relations of entanglement play an important role in quantum systems, however, most of them are given in summation form. In this paper, we investigate the product-form monogamy relations of multipartite entanglement in terms of the [Formula: see text]th power of concurrence and negativity. Compared with the existing monogamy relations, the product-form monogamy relations of multi-body quantum entanglement have a stricter lower bound.
Monogamy of entanglement essentially characterizes the entanglement distributions among the subsystems. Generally it is given by summation-form monogamy inequalities. In this paper, we present the product-form monogamy inequalities satisfied by the ννν-th (ν≥2ν\geq2ν≥2) power of the concurrence. We show that they are tighter than the existing ones by detailed example. We then establish tighter product-form monogamy inequalities based on the negativity. We show that they are valid even for high dimensional states to which the well-known CKW inequality is violated.
Abstract Quantum entanglement in multipartite systems exhibits a unique restriction on its distribution among subsystems, a fundamental property known as the monogamy of entanglement. Traditionally, monogamy has been quantified for measures such as concurrence through summation-form inequalities. Recently, it has been discovered that concurrence also obeys monogamy constraints expressed via product-form inequalities. In this work, we establish enhanced monogamy inequalities for the ν th power of concurrence (with ν ⩾ 2 ). We demonstrate, through explicit examples, that these new inequalities provide tighter bounds than existing product-form results. Furthermore, we show that our findings remain applicable to monogamy relations in high-dimensional systems.
The entanglement in multipartite quantum system is hard to characterize and quantify, although it has been intensively studied in bipartite systems. The monogamy of entanglement, as a special property of multipartite systems, shows the distribution of entanglement in the system. In this paper, we investigate the monogamy relations for multi-qubit systems. By using two entangled measures, namely the concurrence C and the negativity Nc, we establish tighter monogamy inequalities for their α-th power than those in all the existing ones. We also illustrate the tightness of our results for some classes of quantum states.
Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations related to the concurrence CCC, the entanglement of formation EEE, negativity Nc{N}_{c}Nc​, and Tsallis-qqq entanglement Tq{T}_{q}Tq​. Monogamy relations for the $\ensuremath{\alpha}\mathrm{th}$ power of entanglement have been derived, which are tighter than the existing entanglement monogamy relations for some classes of quantum states. Detailed examples are presented.