Concurrence of assistance and Mermin inequality on three-qubit pure states

Deterministic Entanglement of Assistance and Monogamy Constraints

Certain quantum information tasks require entanglement of assistance, namely a reduction of a tripartite entangled state to a bipartite entangled state via local measurements. We establish that 'concurrence of assistance' (CoA) identifies capabilities and limitations to producing pure bipartite entangled states from pure tripartite entangled states and prove that CoA is an entanglement monotone for $(2\times2\times n)$-dimensional pure states. Moreover, if the CoA for the pure tripartite state is at least as large as the concurrence of the desired pure bipartite state, then the former may be t…

Monogamy relations of concurrence for any dimensional quantum systems

We study monogamy relations for arbitrary dimensional multipartite systems. Monogamy relations based on concurrence and concurrence of assistance for any dimensional $m_1\otimes m_2\otimes...\otimes m_{N}$ quantum states are derived, which give rise to the restrictions on the entanglement distributions among the subsystems. Besides, we give the lower bound of concurrence for four-partite mixed states. The approach can be readily generalized to arbitrary multipartite systems.

Generalized Monogamy Relations of Concurrence for N-qubit Systems

We present a new kind of monogamous relations based on concurrence and concurrence of assistance. For $N$-qubit systems $ABC_1...C_{N-2}$, the monogamy relations satisfied by the concurrence of $N$-qubit pure states under the partition $AB$ and $C_1...C_{N-2}$, as well as under the partition $ABC_1$ and $C_2...C_{N-2}$ are established, which give rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.

Bipartite concurrence and localized coherence

Based on a proposed coherence measure, we show that the local coherence of a bipartite quantum pure state (coherence of its reduced density matrix) is exactly the same as the minimal average co- herence with all potential pure-state realizations under consideration. In particular, it is shown that bipartite concurrence of pure states just captures the maximal difference between local coherence and the average coherence of one subsystem induced by local operations on the other subsystem with the assistance of classical communications, which provides an alternative operational meaning for bipart…

Polygamy relations of multipartite systems

We investigate the polygamy relations of multipartite quantum states. General polygamy inequalities are given in the $α$th $(α\geq 2)$ power of concurrence of assistance, $β$th $(β\geq1)$ power of entanglement of assistance, and the squared convex-roof extended negativity of assistance (SCRENoA).

Polygamy relations of multipartite entanglement beyond qubits

We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the $α$th $(0\leq α\leq 2)$ power of concurrence of assistance is first presented for multipartite pure states in arbitrary-dimensional quantum systems. We further show that the general polygamy inequalities can even be improved to be tighter inequalities under certain conditions on the assisted entanglement of bipartite subsystems. Based on the improved polygamy relations, lower bound for distribution of bipartite entanglement is provided in a…

Monogamy Relations for the Generalized W Class

Here we investigate the monogamy relations for the generalized W class. Monogamy inequalities for the generalized W class in terms of the $β$-th ($β\in (0,2)$) power of the concurrence, the concurrence of assistance and the negativity are presented. At last, under some restricted conditions of the generalized W class, we present stronger monogamy inequalities.

Characterization of entanglement of more than two qubits with Bell inequalities and global entanglement

It is shown that the entanglement-structure of 3- and 4-qubit states can be characterized by optimized operators of the Mermin-Klyshko type. It is possible to discriminate between pure 2-qubit entanglements and higher entanglements. A comparison with a global entanglement measure and the i-concurrence is made.

Direct versus measurement assisted bipartite entanglement in multi-qubit systems and their dynamical generation in spin systems

We consider multi-qubit systems and relate quantitatively the problems of generating cluster states with high value of concurrence of assistance, and that of generating states with maximal bipartite entanglement. We prove an upper bound for the concurrence of assistance. We consider dynamics of spin-1/2 systems that model qubits, with different couplings and possible presence of magnetic field to investigate the appearance of the discussed entanglement properties. We find that states with maximal bipartite entanglement can be generated by an XY Hamiltonian, and their generation can be controll…

General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States

Entanglement monogamy is a fundamental property of multipartite entangled states. We investigate the monogamy relations for multiqubit generalized W-class states. Analytical monogamy inequalities are obtained for the concurrence of assistance, the entanglement of formation and the entanglement of assistance.

G_q-并发度与多量子比特系统中的纠缠约束

G_q-concurrence and entanglement constraints in multiqubit systems

本文提出$G_q$-并发度作为并发度的推广，证明其满足纠缠度量公理，并利用其平方的单夫不等式构造纠缠指示器，以检测多量子比特系统中的真正纠缠态。

Tighter monogamy relations of quantum entanglement for multiqubit W-class states

Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations for multiqubit generalized W-class states. We present new analytical monogamy inequalities for the concurrence of assistance, which are shown to be tighter than the existing ones. Furthermore, analytical monogamy inequalities are obtained for the negativity of assistance.

Tripartite Entanglement and Quantum Correlation

We provide an analytical tripartite-study from the generalized $R$-matrix. It provides the upper bound of the maximum violation of Mermin's inequality. For a generic 2-qubit pure state, the concurrence or $R$-matrix characterizes the maximum violation of Bell's inequality. Therefore, people expect that the maximum violation should be proper to quantify Quantum Entanglement. The $R$-matrix gives the maximum violation of Bell's inequality. For a general 3-qubit state, we have five invariant entanglement quantities up to local unitary transformations. We show that the five invariant quantities de…

Tighter generalized monogamy and polygamy relations for multiqubit systems

We present a different kind of monogamy and polygamy relations based on concurrence and concurrence of assistance for multiqubit systems. By relabeling the subsystems associated with different weights, a smaller upper bound of the $α$th ($0\leqα\leq2$) power of concurrence for multiqubit states is obtained. We also present tighter monogamy relations satisfied by the $α$th ($0\leqα\leq2$) power of concurrence for $N$-qubit pure states under the partition $AB$ and $C_1 . . . C_{N-2}$, as well as under the partition $ABC_1$ and $C_2\cdots C_{N-2}$. These inequalities give rise to the restrictions…

三量子比特系统中的辅助纠缠

Entanglement of assistance in three-qubit systems

本文研究三量子比特系统的辅助纠缠，发现以局域生成Bell态的最大概率度量纠缠时辅助方无损解耦总可行，而对多数其他纠缠度量仅特殊态族可实现并完成其表征。

内部、辅助和外部纠缠之间的紧致权衡

Tight Trade-off Between Internal, Assisted, and External Entanglement

研究提出三粒子纯态中纠缠与辅助纠缠之和的紧致界，揭示内部纠缠与环境诱导纠缠间的精确权衡关系。

广义单配性与多配性关系的更紧界

Tighter bounds for generalized monogamy and polygamy relations

本文提出参数化界方法，统一改进多体量子系统中辅助并发与辅助负性的广义单配性和多配性关系，克服了旧方法区域局限，并在所有区域有效。

Monogamy relations of all quantum correlation measures for multipartite quantum systems

The monogamy relations of quantum correlation restrict the sharability of quantum correlations in multipartite quantum states. We show that all measures of quantum correlations satisfy some kind of monogamy relations for arbitrary multipartite quantum states. Moreover, by introducing residual quantum correlations, we present tighter monogamy inequalities that are better than all the existing ones. In particular, for multi-qubit pure states, we also establish new monogamous relations based on the concurrence and concurrence of assistance under the partition of the first two qubits and the remai…

Entanglement Monogamy of Tripartite Quantum States

An interesting monogamy equation with the form of Pythagorean theorem is found for $2\otimes 2\otimes n$-dimensional pure states, which reveals the relation among bipartite concurrence, concurrence of assistance, and genuine tripartite entanglement. At the same time, a genuine tripartite entanglement monotone as a generalization of 3-tangle is naturally obtained for $(2\otimes 2\otimes n)$- dimensional pure states in terms of a distinct idea. For mixed states, the monogamy equation is reduced to a monogamy inequality. Both results for tripartite quantum states can be employed to multipartite q…

Svetlichny's inequality and genuine tripartite nonlocality in three-qubit pure states

The violation of the Svetlichny's inequality (SI) [Phys. Rev. D, 35, 3066 (1987)] is sufficient but not necessary for genuine tripartite nonlocal correlations. Here we quantify the relationship between tripartite entanglement and the maximum expectation value of the Svetlichny operator (which is bounded from above by the inequality) for the two inequivalent subclasses of pure three-qubit states: the GHZ-class and the W-class. We show that the maximum for the GHZ-class states reduces to Mermin's inequality [Phys. Rev. Lett. 65, 1838 (1990)] modulo a constant factor, and although it is a functio…

辅助纠缠作为多方纠缠的度量

Entanglement of Assistance as a measure of multiparty entanglement

针对多方纠缠量化的挑战，提出辅助体积（VoA）度量，通过计算所有潜在参与方辅助纠缠的几何平均值，可区分MPC无法区分的态且为GGM的上界，在量子信息处理中具有实际效用。

Relation between entanglement measures and Bell inequalities for three qubits

For two qubits in a pure state there exists a one-to-one relation between the entanglement measure (the concurrence ${\cal C}$) and the maximal violation ${\cal M}$ of a Bell inequality. No such relation exists for the three-qubit analogue of ${\cal C}$ (the tangle $τ$), but we have found that numerical data is consistent with a simple set of upper and lower bounds for $τ$ given ${\cal M}$. The bounds on $τ$ become tighter with increasing ${\cal M}$, so they are of practical use. The Svetlichny form of the Bell inequality gives tighter bounds than the Mermin form. We show that the bounds can b…

Measurable entanglement for tripartite quantum pure states of qubits

We show that for tripartite quantum pure states of qubits, all the kinds of entanglement in terms of SLOCC classification are experimentally measurable by simple projective measurements, provided that four copies of the composite quantum system are available. In particular, the entanglement of reduced density matrices, even though they are mixed states, can be exactly determined in experiment. Concurrence of assistance is also shown to be measurable by introducing an interesting equations with explicit physical meanings.

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。

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

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。