arXiv 2203.166292022-03-30quant-ph

A new parameterized monogamy relation between entanglement and equality

Zhi-Xiang Jin, Shao-Ming Fei, Xianqing Li-Jost, Cong-Feng Qiao

发表信息：: Adv. Quantum Technol. 2022, 2100148

英文摘要：

We provide a generalized definition of the monogamy relation for entanglement measures. A monogamy equality rather than the usual inequality is presented based on the monogamy weight, from which we give monogamy relations satisfied by the $α$th $(α>0)$ power of the entanglement measures. Taking concurrence as an example, we further demonstrate the significance and advantages of these relations. In addition, we show that monogamy relations can be recovered by considering multiple copies of states for every non-additive entanglement measure that violates the inequalities. We also demonstrate that the such relations for tripartite states can be generalized to multipartite systems.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

更紧的参数化单配性关系

Tighter parameterized monogamy relations

本文提出一种系统性的紧化方法，通过引入参数化界族，获得了多体量子系统中比最新研究更紧的单配性关系下界，并通过示例验证了其优越性。

2024-07-25quant-ph

Monogamy equality in $2\otimes 2 \otimes d$ quantum systems

There is an interesting property about multipartite entanglement, called the monogamy of entanglement. The property can be shown by the monogamy inequality, called the Coffman-Kundu-Wootters inequality [Phys. Rev. A {\bf 61}, 052306 (2000); Phys. Rev. Lett. {\bf 96}, 220503 (2006)], and more explicitly by the monogamy equality in terms of the concurrence and the concurrence of assistance, $\mathcal{C}_{A(BC)}^2=\mathcal{C}_{AB}^2+(\mathcal{C}_{AC}^a)^2$, in the three-qubit system. In this paper, we consider the monogamy equality in $2\otimes 2 \otimes d$ quantum systems. We show that $\mathcal…

2008-04-01quant-ph

A monogamy equalities of complementarity relation and distribute entanglement for multi-qubit pure states

We propose a method to detect genuine quantum correlation for multi-qubit pure states. We then derive a complementarity relations for pure quantum states of N qubits. We prove that in all many-qubit systems there exist strict monogamy laws for quantum correlations. On the other hand, it is known that the entanglement monogamy equality proposed by Coffman, Kundu, and Wootters is in general not true for multiqubit states. Inducing from the CKW equality, we find a proper form of entanglement monogamy equality for arbitrary quantum states. The total quantum correlation of qubit k with the remainin…

2016-03-18quant-ph

Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits

We discuss the possibility to interpret the residual entanglement for more than three qubits in terms of distributed multipartite entanglement, or, in other words, possible extensions of the Coffman-Kundu-Wootters monogamy equality to higher qubit numbers. Existing knowledge on entanglement in multipartite systems puts narrow constraints on the form of such extensions. We study various examples for families of pure four-qubit states for which the characterization of three-qubit and four-qubit entanglement in terms of polynomial invariants is known. These examples indicate that, although famili…

2009-04-06cond-mat.otherquant-ph

Multipartite monogamy of the concurrence

Monogamy of entanglement is generally discussed using a bipartite entanglement measure as an upper bound. Here we discuss a new kind of monogamous relation where the upper bound is given by a multipartite measure of entanglement, the generalized concurrence. We show a new monogamous equality involving the multipartite concurrence, all the bipartite concurrences and the genuine tripartite entanglement for pure three qubits system. The result extends to mixed states in an inequality involving the generalized concurrence and all the bipartite concurrences. We provide a counter-example showing tha…

2013-02-05quant-ph

参数化二分纠缠度量与纠缠约束

Parameterized bipartite entanglement measures and entanglement constraints

本文提出参数化纠缠度量 $G_ω$C，证明其公理化性质及两量子比特解析关系，并基于 S$G_ω$C 建立任意 $N$-量子比特混态与高维多体系统的单婚约束及纠缠指标。

2025-03-18quant-ph

更多相关论文收起更多论文

Monogamy of entanglement without inequalities

We provide a fine-grained definition for monogamous measure of entanglement that does not invoke any particular monogamy relation. Our definition is given in terms an equality, as oppose to inequality, that we call the "disentangling condition". We relate our definition to the more traditional one, by showing that it generates standard monogamy relations. We then show that all quantum Markov states satisfy the disentangling condition for any entanglement monotone. In addition, we demonstrate that entanglement monotones that are given in terms of a convex roof extension are monogamous if they a…

2018-08-09math-phmath.MPquant-ph

多体系统的统一一夫一妻制和多配偶制关系

Unified monogamy and polygamy relations for multipartite systems

Guangzhou Maritime University（广州航海学院）；North Carolina State University（北卡罗来纳州立大学）

该研究针对二分纠缠度量及其辅助度量，引入由参数$m$索引的统一框架，推导出两个层次的精细不等式族，随着$m$增加边界收紧，推广并加强了现有关系，为量子相关领域应用提供了增强且灵活的工具。

2026-07-17quant-ph

Entanglement Constraints on States Locally Connected to the Greenberger-Horne-Zeilinger State

The multi-qubit GHZ state possesses tangles with elegant transformation properties under stochastic local operations and classical communication. Since almost all pure 3-qubit states are connected to the GHZ state via SLOCC, we derive a necessary and sufficient achievability inequality on arbitrary 3-qubit tangles, which is a strictly stronger constraint than both the monogamy inequality and the marginal eigenvalue inequality. We then show that entanglement shared with any single party in the n-qubit GHZ SLOCC equivalence class is precisely accounted for by the sum of its k-tangles, recently c…

2017-09-14quant-ph

An equality between entanglement and uncertainty

Heisenberg's uncertainty principle implies that if one party (Alice) prepares a system and randomly measures one of two incompatible observables, then another party (Bob) cannot perfectly predict the measurement outcomes. This implication assumes that Bob does not possess an additional system that is entangled to the measured one; indeed the seminal paper of Einstein, Podolsky and Rosen (EPR) showed that maximal entanglement allows Bob to perfectly win this guessing game. Although not in contradiction, the observations made by EPR and Heisenberg illustrate two extreme cases of the interplay be…

2014-12-22quant-ph

优越的单配性与多配性关系及并发度的估计

Superior monogamy and polygamy relations and estimates of concurrence

本文以统一方式提出更紧的两体纠缠单配性与多配性关系上下界，并利用CoA多配性关系获得了任意N量子比特纯态并发度的良好估计。

2025-03-02quant-ph

多体量子系统的纠缠度量：局限性与新方法

Entanglement measures for multipartite quantum systems:limitations and new approaches

Shahid Chamran University of Ahvaz（阿瓦士沙希德·恰姆兰大学）

针对某些量子态（如广义W态）中传统纠缠度量（单纠缠、π纠缠）随粒子数增加而失效的问题，提出了三种替代度量（两纠缠和、单纠缠平方和、广义剩余纠缠）和强纠缠单配性。

2026-08-18quant-ph

Quantum correlation via quantum coherence

Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition--------quantum coherence or quantum superposition. In this paper, we attempt to give an alternative understanding of how quantum correlation is related to quantum coherence. We divide the coherence of a quantum state into several classes and find the complete coincidence between geometric (symmetric and asymmetric) quantum discords and some particular classes of quantum coherence. We propose a revised measure for total coherence and find that this measure can l…

2014-02-19quant-ph

结构f-散度：参数化量子电路参数空间中成本函数矩和梯度的紧致通用界限

Structural $f$-divergence: Tight universal bounds for cost function moments and gradients in parameterized quantum circuits

本文提出结构f-散度，用于分析参数化量子电路参数空间中成本函数矩和梯度的紧致通用界限，通过单个量子比特单层结构实现等式条件，为避免 barren plateau 和成本集中提供必要条件，同时抑制噪声诱导偏差。

2026-05-18quant-ph

逐个量子猜测：超越纠缠一夫一妻制（MoE）游戏的多体纠缠

One-at-a-Time Quantum Guessing: Multipartite Entanglement Beyond MoE Games

Department of Electrical and Computer Engineering, Rutgers, the State University of New Jersey（新泽西州立大学罗格斯分校电气与计算机工程系）

本文引入逐个猜测（OTG）游戏作为研究多体纠缠有用性的新框架，发现其在泡利测量场景中可使获胜概率至少提高4%，且游戏价值遵循玩家选择概率分布的优超顺序。

2026-08-19cs.ITmath.ITquant-ph

基于总纠缠度的新一种纠缠度量

A new entanglement measure based on the total concurrence

本文提出基于总纠缠度的新纠缠度量$\mathcal{C}^{t}_q$和$\mathcal{C}^{t}_α$，并推导了其解析表达式和下界，研究了其在双ubit系统中的结合关系。

2025-12-30quant-ph