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arXiv:2007.09544 · Laser Physics Letters

Strong superadditivity relations for multiqubit systems

Xianfei Qi, Ting Gao, Fengli Yan, Yan Hong

Published Sep 7, 2020• 2 citations
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Abstract

Abstract We investigate the distributions of quantum coherence characterized by superadditivity relations in multipartite quantum systems. General superadditivity inequalities based on the α th ( α ⩾ 1 ) power of l 1 norm of coherence are presented for multiqubit states, which include the existing ones as special cases. Our result is shown to be tighter than the existing one by a specific example.

DOI
10.1088/1612-202x/abae02

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Abstract We investigate the distributions of quantum coherence characterized by superadditivity relations in multipartite quantum systems. General superadditivity inequalities based on the α th ( α ⩾ 1 ) power of l 1 norm of coherence are presented for multiqubit states, which include the existing ones as special cases. Our result is shown to be tighter than the existing one by a specific example.
Quantum coherence serves as a crucial physical resource, with its quantification emerging as a focal point in contemporary research. Superadditivity constitutes one of the most fundamental attributes in characterizing the coherence distribution in multipartite quantum systems. In this paper, we provide a way to derive tighter superadditivity inequalities of [Formula: see text]-norm coherence measure for arbitrary multiqubit states. We present a category of superadditivity relations related to the [Formula: see text]th [Formula: see text] power of [Formula: see text]-norm coherence [Formula: see text] under certain conditions. Our results are better than the existing ones and are illustrated in detail with examples.
We study the distribution of quantum correlations characterized by monogamy relations in multipartite systems. By using the Hamming weight of the binary vectors associated with the subsystems, we establish a class of monogamy inequalities for multiqubit entanglement based on the α\alphaαth (α≥2\alpha\geq 2α≥2) power of concurrence, and a class of polygamy inequalities for multiqubit entanglement in terms of the β\betaβth (0≤β≤20\leq \beta\leq20≤β≤2) power of concurrence and concurrence of assistance. Moveover, we give the monogamy and polygamy inequalities for general quantum correlations. Application of these results to quantum correlations like squared convex-roof extended negativity (SCREN), entanglement of formation and Tsallis-qqq entanglement gives rise to either tighter inequalities than the existing ones for some classes of quantum states or less restrictions on the quantum states. Detailed examples are presented.
Abstract In this paper, we investigate the convex roof measures of quantum coherence, with a focus on their superadditive properties. We propose sufficient conditions and establish a framework for coherence superadditivity in tripartite and multipartite systems. Through theoretical derivation, the relevant theorems are given. These results not only expand our understanding of the superadditivity of pure and mixed states but also characterize the conditions under which the superadditivity relations reach equality. Finally, the proposed methods and conclusions are verified through representative examples, providing new theoretical insights into the distribution of quantum coherence in multipartite systems.
In this paper, we investigate the convex roof measure of quantum coherence, with a focus on their superadditive properties. We propose sufficient conditions and establish a framework for coherence superadditivity in tripartite and multipartite systems. Through theoretical derivation, the relevant theorems are given. These results not only expand our understanding of the superadditivity of pure and mixed states but also characterize the conditions under which the superadditivity relations reach equality. Finally, the proposed methods and conclusions are verified through representative examples, providing new theoretical insights into the distribution of quantum coherence in multi-part 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.