Entanglement conditions for multi-mode states
Zong-Guo Li, Shao-Ming Fei, Zhi-Xi Wang, Ke Wu
我们提供了一类不等式检测纠缠多模系统。给出了完全可分、双可分的必要条件和完全纠缠态的充分条件。
We provide a class of inequalities for detecting entanglements in multi-mode systems. Necessary conditions for fully separable, bi-separable and sufficient conditions for fully entangled states are explicitly presented.
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General polygamy inequality of multi-party quantum entanglement
利用辅助纠缠，建立了任意维量子系统中多方纠缠的一般性多配偶不等式。对于多方封闭的量子系统，我们将我们的结果与一夫一妻的纠缠联系起来，说明纠缠熵是一个普遍的纠缠度量，它限制了多方量子纠缠的一夫一妻和一夫多妻.
We present a class of tight monogamy relations in terms of Rényi-$α$ entanglement, which are tighter than the monogamy relations of multiqubit entanglement just based on the power of the Rényi-$α$ entanglement for $α\geq 2$ and the power $η>1$. For $2>α\geq\frac{\sqrt{7}-1}{2}$ and the power $η>2$, we establish a class of tight monogamy relations of multiqubit entanglement with larger lower bounds than the existing monogamy relations of multiqubit entanglement.
Unified entropy, entanglement measures and monogamy of multi-party entanglement
我们证明了多量子比特纠缠的受限共享性可以用统一的$(q,s)$熵来充分刻画。给出了一类双参数的二体纠缠测度，即统一的$(q,s)$纠缠及其在两量子比特系统中的解析公式，分别是$q\geq 1$，$0\leq s \leq1$和$qs\leq3$ .利用统一的$(q,s)$纠缠，建立了$q\geq2$，$0\leq s \leq1$和$qs\leq3$的多量子比特纠缠的一夫一妻不等式.
Sperner state and multipartite entanglement signals
本文提出Sperner状态分类方案，通过多体纠缠度量空间量化多体纠缠结构并实现统一分类。
Lower bounds on the squashed entanglement for multi-party systems
针对多体系统压缩纠缠的评估问题，本文提出可计算的下界，并推导了压缩纠缠与其他纠缠度量间的关联不等式，为多体纠缠度量研究提供有效工具。
Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-$q$ entanglement and Rényi-$α$ entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.
Genuine multipartite entanglement measures based on multi-party teleportation capability
本文针对多体纠缠作为多方量子信息资源的度量问题，基于多方隐形传态能力提出三量子比特及 N 量子比特系统的真正多体纠缠度量，并验证其满足相关公理要求。
We establish a characterization of multi-qubit entanglement constraints in terms of non-negative power of entanglement measures based on unified-$(q,s)$ entropy. Using the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of tight monogamy inequalities of multi-qubit entanglement based on the $α$th-power of unified-$(q,s)$ entanglement for $α\geq 1$. For $0 \leq β\leq 1$, we establish a class of tight polygamy inequalities of multi-qubit entanglement in terms of the $β$th-power of unified-$(q,s)$ entanglement of assistance. Thus our results c…
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.
Detecting multilevel entanglement from light-based entanglement witnesses
本文提出了一种基于电场的不等式，用于检测多级纠缠，适用于多体量子系统。
Spatial multipartite entanglement and localization of entanglement
我们提出了一个简单的模型，连同它的物理实现，它允许一个产生多体纠缠之间的几个空间模式的电磁场。它是基于参数下转换与N对垂直倾斜的平面波作为一个泵。在零相位失配和非零相位失配的情况下，研究了这种空间纠缠的特性。进一步研究了两个空间模的纠缠局域化现象，结果表明纠缠增强了N的平方根。
We investigate the monogamy relations related to the concurrence, the entanglement of formation, convex-roof extended negativity, Tsallis-q entanglement and R'enyi-α entanglement, the polygamy relations related to the entanglement of formation, Tsallis-q entanglement and R'enyi-α entanglement. Monogamy and polygamy inequalities are obtained for arbitrary multipartite qubit systems, which are proved to be tighter than the existing ones. Detailed examples are presented.
The Schmidt-decomposition formalism is proposed to be used for evaluation of the degree of quadrature entanglement in two-mode multiphoton states.
Entanglement in a class of multiqubit mixed states without multipartite tangles
基于量子互补关系（QCR）和一个纯化方案，我们分析了一类纠缠但没有两个和真正的三个，四个，.的N比特混合态，N量子位纠缠结果表明，这些混合态的纠缠度（单纠缠度或负纠缠度）与其纯态的QCR纠缠度密切相关。特别地，阐述了当混合态不存在多体纠缠（二体及以上纠缠）时，它的纠缠实际上是系统与环境之间的一种真正的多体QCR纠缠.
Entanglement shared among multiple parties presents complex challenges for the characterisation of different types of entanglement. One of the most fundamental insights is the fact that some mixed states can feature entanglement across every possible cut of a multipartite system yet can be produced via a mixture of states separable with respect to different partitions. To distinguish states that genuinely cannot be produced from mixing such partition-separable states, the term genuine multipartite entanglement was coined. All these considerations originate in a paradigm where only a single cop…
We investigate the tight monogamy and polygamy relations of multiparty entanglement for arbitrary quantum states. By using the power of the bipartite measure of entanglement, we establish a class of tight monogamy relations of multiparty entanglement with larger lower bounds than the existing monogamy relations. We also give a class of tight polygamy relations of multiparty entanglement with smaller upper bounds than the existing polygamy relations, by using the power of the entanglement of assistance. It is shown that these new monogamy and polygamy relations are tighter than the former resul…
A class of entanglement monotones for general pure multipartite states based on complex projective variety
基于Segre簇，我们构造了一般纯多体态的纠缠度量。基于格拉斯曼簇的Plücker坐标方程，我们还构造了一类纠缠单调.此外，我们讨论和比较这些措施的纠缠。
Monogamy and polygamy for multi-qubit entanglement using Rényi entropy
利用$α$熵量化两体纠缠，证明了多量子比特系统中$α\geq 2$的纠缠是单偶的.我们还猜想了一个多量子比特纠缠的多偶不等式，并给出了$0.83-ε\leq α\leq 1.43+ε$与$0<ε<0.01$的强数值证据.
Multi-impurity effects on the entanglement of anisotropic Heisenberg ring XXZ under a homogeneous magnetic field
研究了均匀磁场中多杂质对各向异性海森堡环XXZ纠缠度的影响。杂质使环中相等的两两纠缠相互竞争，使两两纠缠出现振荡。如果杂质具有较大的耦合，则临界温度和两两纠缠度都可以得到改善
Entanglement monotones for multi-qubit states based on geometric invariant theory
基于Grassmann簇的Plücker坐标方程，构造了多量子比特态的纠缠单调性.作为一个说明性的例子，我们详细研究了三量子比特态的纠缠单调性。
We provide a sufficient condition for the monogamy inequality of multi-party quantum entanglement of arbitrary dimensions in terms of entanglement of formation. Based on the classical-classical-quantum(ccq) states whose quantum parts are obtained from the two-party reduced density matrices of a three-party quantum state, we show the additivity of the mutual information of the ccq states guarantees the monogamy inequality of the three-party pure state in terms of EoF. After illustrating the result with some examples, we generalize our result of three-party systems into any multi-party systems o…
Tsallis entropy and entanglement constraints in multi-qubit systems
我们证明了Tsallis- $q$熵可以刻画多量子比特纠缠的受限共享性和分布.首先给出了一类二体纠缠度量Tsallis- $q$纠缠，并给出了它在两量子比特系统中的解析表达式。对于$2 \leq q \leq 3$，我们用Tsallis- $q$纠缠给出了多量子比特纠缠的一夫一妻不等式，并且用Tsallis- $q$熵给出了$1 \leq q \leq 2$和$3 \leq q \leq 4$的一夫多妻不等式.
An Equivalence of Entanglement-Assisted Transformation and Multiple-Copy Entanglement Transformation
我们研究了纠缠辅助变换和多拷贝纠缠变换的能力。首先，我们找到了一个充分条件，当一个给定的催化剂是有用的，在生产另一个特定的目标状态。作为这个条件的应用，对于任意非最大纠缠的二体纯态和任意不小于4的整数$n$，我们可以显式地构造出一组$n\times n$量子态，这些量子态可以由给定的态作为催化剂产生.其次，我们证明了对于任何正整数$k$，利用$k\times k$维催化剂的纠缠辅助变换在产生目标态中是有用的当且仅当利用$k$态拷贝的多拷贝纠缠变换在产生相同的目标中是有用的。此外，还根据目标的Schmidt系数，得到了两者都成立的一个充分必要条件。这种纠缠辅助变换与多拷贝纠缠变换的等价性暗示了纠缠变换的许多有趣性质。此外，这些结果被推广到概率纠缠变换的情况。
Characterizing the combinatorics of distributed EPR pairs for multi-partite entanglement
我们开发的协议准备GHZ状态，在一般情况下，一个纯粹的多部最大纠缠态在一个分布式网络中的先验量子纠缠代理之间使用经典的通信和本地操作。我们调查和特征的最小组合学的共享EPR对之间的代理在网络中创建多方纠缠。我们还描述了最小组合的代理在创建纯最大多方纠缠之间的一组$N$的$n$代理在网络中使用先验多方纠缠状态之间的子集$N$。我们提出了在上述情况下建立多方纠缠的协议。
We interpret multi-partite genuine entanglement witnesses as simultaneous positivity of various maps arising from them. We apply this result to multi-qubit {\sf X}-shaped Hermitian matrices, and characterize the conditions for them to be genuine entanglement witnesses, in terms of entries. Furthermore, we find all optimal ones among them. They turn out to have the spanning properties, and so they detect non-zero volume set of multi-qubit genuine entanglement. We also characterize decomposability for {\sf X}-shaped entanglement witnesses.
Hierarchies of multi-partite entanglement
我们推导出分层标准，确定不同程度的纠缠范围从两部分真正的多部分在任意大小的混合量子态。
Entanglement tensor for a general pure multipartite quantum state
我们提出了一个纠缠张量来计算一般纯多体量子态的纠缠。我们比较了由此产生的张量与二分态的纠缠度，并将张量测度应用到一些有趣的三量子比特和四量子比特纠缠态的例子中。它表明，在定义的纠缠度的多方状态，需要作出假设的各方合作的意愿。我们还讨论了多量子比特$\ket{W_{M}}$态的纠缠度。
We study the generation of entanglement induced by a single-photon Gaussian wavepacket in multi-atom bi-directional waveguide QED. In particular, we investigate the effect of increasing the number of atoms on the average pairwise entanglement. We demonstrate by selecting smaller decay rates and in chiral waveguide settings, that both entanglement survival times and maximum generated entanglement can be increased by at least a factor of 3/2, independent of the number of atoms. In addition, we analyze the influence of detuning and delays on the robustness of the generated entanglement. There are…
Entanglement detection length of multipartite quantum states
本文提出纠缠检测长度概念，刻画检测真正多体纠缠所需联合测量的最少粒子数，并利用边际态可分性检验和半定规划方法给出确定方式与上界。
Entanglement witnesses and concurrence for multi-qubit states
我们建立了并发和纠缠证人之间的关系。特别地，我们利用纠缠度和不同的算符集构造了三比特W态和GHZ态的纠缠见证，并将其推广到多比特态.
Improved criteria of detecting multipartite entanglement structure
本文利用张量积空间划分构造纠缠见证，并结合半定规划与梯度下降算法，提出改进的多体纠缠结构检测判据，实验表明其性能优于现有方法。
We prove a new polygamy relation of multi-party quantum entanglement in terms of Rényi-$α$ entanglement of assistance for $\left( {\sqrt 7 - 1} \right)/2\leqα\leq \left( {\sqrt 13 - 1} \right)/2$. This class of polygamy inequality reduces to the polygamy inequality based on entanglement of assistance since Rényi-$α$ entanglement is a generalization of entanglement of formation. We further show that the polygamy inequality also holds for the $μ$th power of Rényi-$α$ entanglement of assistance.
Tsallis-$q$ entanglement is a bipartite entanglement measure which is the generalization of entanglement of formation for $q$ tending to 1. We first expand the range of $q$ for the analytic formula of Tsallis-\emph{q} entanglement. For $\frac{5-\sqrt{13}}{2} \leq \emph{q} \leq \frac{5+\sqrt{13}}{2}$, we prove the monogamy relation in terms of the squared Tsallis-$q$ entanglement for an arbitrary multi-qubit systems. It is shown that the multipartite entanglement indicator based on squared Tsallis-$q$ entanglement still works well even when the indicator based on the squared concurrence loses i…
Macroscopic Observables Detecting Genuine Multipartite Entanglement and Partial Inseparability in Many-Body Systems
本文给出了一种仅通过宏观观测量（如能量）来检测多体系统中真正的多体纠缠和部分不可分性的一般方法。我们表明，所获得的标准，“GME间隙”和“的k-纠缠间隙”，检测大面积的真正的多体纠缠和部分纠缠在典型的多体状态，这是没有检测到的其他标准。由于真实的多体纠缠是一些量子信息理论应用的必要性质，例如秘密共享或某些种类的量子计算，我们的方法可以用来选择或设计适当的凝聚态系统。
The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems
我们回顾和推广了最近引入的框架熵矢量检测和量化真正的多体纠缠在高维多组分量子系统。我们表明，这些想法可以扩展到其他形式的多体纠缠之间的歧视。特别地，我们开发了测试密度矩阵是否可分解的方法，即：e.相对于子系统的某些给定分区是可分离的; $k$ -可分离的，即e.相对于子系统的$k$分区是可分离的; $k$ -部分纠缠，即在至少$k$方的子集之间存在纠缠。我们还讨论了如何评估在所有这些情况下的纠缠的维数。
Multi-Qubit Systems: Highly Entangled States and Entanglement Distribution
比较了基于不同纠缠度量或纠缠指标的高纠缠多比特态的各种搜索方法。特别地，我们目前的结果与Brown等人最近报道的结果进行了比较[J. Phys. A：Math.Gen.38（2005）1119]。本文还研究了上述多量子比特系统纠缠度的统计分布。
Detecting genuine multipartite entanglement of pure states with bipartite correlations
对于任意的纯多量子比特态，二体关联的一夫一妻制导致能够通过排除k-可分性的可能性来指示各种类型的多体纠缠的简单条件。
Correlation tensor criteria for genuine multiqubit entanglement
我们提出了一个发展的纠缠指标的几何方法。该方法被应用于检测真正的多量子比特纠缠。该准则以施加在相关张量上的非线性条件的形式给出。因此，它们涉及直接可观察的量，并且在某些情况下，只需要很少的特定测量就可以找到多量子比特纠缠。每个标准的非线性允许在宽类状态中检测纠缠。与在厄米算符空间中定义超平面的纠缠见证相反，新条件定义了一个几何图形，将非完全纠缠态封装在其中。
Multiparticle entanglement in graph-diagonal states: Necessary and sufficient conditions for four qubits
真实多粒子纠缠的表征对于纠缠理论以及量子信息理论的实验研究都具有重要意义。在这里，我们完全描述了真正的多粒子纠缠的四量子比特状态对角的集群状态的基础。此外，我们给出了一个完整的多粒子纠缠特性的所有五个量子比特的图形状态混合白噪声，状态对角线的基础上对应的五个量子比特的Y形图，和一个家庭的图形状态与任意数量的量子比特。
We investigate polygamy relations of multipartite entanglement in arbitrary-dimensional quantum systems. By improving an inequality and using the $β$th ($0\leqβ\leq1$) power of entanglement of assistance, we provide a new class of weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems. We show that these new polygamy relations are tighter than the ones given in [Phys. Rev. A 97, 042332 (2018)].
Creating and preserving multi-partite entanglement with spin chains
我们展示了如何在分支自旋链系统中产生多体纠缠，如W态形式。我们还讨论了保存这种纠缠，一旦创建。该技术可以应用于实际的自旋链系统，或其他物理系统，如耦合量子点，分子或原子串。
We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order $q$, we first provide a generalized monogamy inequality of multi-qubit entanglement for $q=2$ or $3$. This generalization encapsulates multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-$q$ entropy for $1 \leq q \leq2$ or $3 \leq q \leq 4$, which also contains the multi-qubit polygamy inequality as a special case.
Local Invariants and Pairwise Entanglement in Symmetric Multi-qubit System
利用完备的两量子比特局域不变量分析了对称多量子比特系统的两两纠缠特性。用不变量表示纠缠的集体特征，如自旋压缩，并提出了一种两两纠缠的分类方案。这里给出的不变的标准示出有关最近提出的（物理评论快报。95，120502（2005））对称多比特态中两两纠缠的广义自旋压缩不等式。
Entanglement entropy in quasi-symmetric multi-qubit states
我们将对称多比特态推广到它们的q-类似态，其基矢与q-Dicke态相同。我们研究了这些态的纠缠熵，发现由于q形变引起的不均匀性，纠缠被挤出到系统的某些区域。我们还计算了一个相关的q变形Lipkin-Meshkov-Glick模型基态的纠缠熵，并证明了在不同的q变形强度下，纠缠的奇异性可以正确地表征量子相变点.
We provide a strong evidence for strong monogamy inequality of multi-qubit entanglement recently proposed in [B. Regula {\em et al.}, Phys. Rev. Lett. {\bf 113}, 110501 (2014)]. We consider a large class of multi-qubit generalized W-class states, and analytically show that the strong monogamy inequality of multi-qubit entanglement is saturated by this class of states.
Entanglement witnesses based on first and second moments exist in the form of spin-squeezing criteria for the detection of particle entanglement from collective measurements, and in form of modified uncertainty relations for the detection of mode entanglement or steering. By revealing a correspondence between them, we show that metrologically useful spin squeezing reveals multimode entanglement in symmetric spin states that are distributed into addressable modes. We further derive tight state-independent multipartite entanglement bounds on the spin-squeezing coefficient and point out their con…
We introduce two independent quantifications for 3-mode and 4-mode entanglement. We investigate the conversion of one type of nonclassicality, i.e. single-mode nonclassicality, into another type of nonclassicality, i.e. multi-mode entanglement, in beam-splitters. We observe parallel behavior of the two quantifications. The methods can be generalized to the quantification of any multi-mode entanglement.
Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
我们研究了多尺度纠缠重整化模型（MERA）及其推广的分支MERA中纠缠熵的标度性。我们提供了这种缩放的分析上限，它采取的一般形式的边界法律与各种类型的乘法校正，包括幂律校正所有的方式散装法律。对于感兴趣的几种情况下，我们还提供了数值结果表明，这些上限是饱和的领导秩序。特别是，我们建立，通过适当的选择全息树，分支MERA可以重现在$D\geq 2$维费米液体和自旋玻色金属中观察到的边界定律的对数乘法校正。
We propose the usage of persistent homologies to characterize multipartite entanglement. On a multi-qubit data set we introduce metric-like measures defined only in terms of bipartite entanglement and then we derive barcodes. We show that they are able to provide a good classification of entangled states, at least for a small number of qubit.
The multimode nature of spacetime entanglement in QFT
本文证明了四维平坦时空中自由无质量标量量子场真空态存在因果断开区域间的多模态纠缠，指出其虽在单模态下稀疏但整体无处不在，且可操作提取并构成纠缠提取协议的基础。
Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case of pure multi-particle quantum states, features of the global entanglement can already be extracted from local information alone. This is achieved by associating with any given class of entanglement an entanglement polytope---a geometric object which characterizes the single-particle states compatible with that class. Our results, applicable to systems of a…
We posit a geometrical description of the entanglement of purification for subregions in a holographic CFT. The bulk description naturally generalizes the two-party case and leads to interesting inequalities among multi-party entanglements of purification that can be geometrically proven from the conjecture. Further, we study the relationship between holographic entanglements of purification in locally-AdS3 spacetimes and entanglement entropies in multi-throated wormhole geometries constructed via quotienting by isometries. In particular, we derive new holographic inequalities for geometries t…
We study the evolution of multi-region bipartite entanglement entropy under locally scrambled quantum dynamics. We show that the multi-region entanglement can significantly modify the growth of single-region entanglement, whose effect has been largely overlooked in the existing literature. We developed a novel theoretical framework, called the entanglement feature formalism, to organize all the multi-region entanglement systematically as a sign-free many-body state. We further propose a two-parameter matrix product state (MPS) ansatz to efficiently capture the exponentially many multi-region e…
Macroscopic Multi-Species Entanglement near Quantum Phase Transitions
多粒子纠缠是指多粒子系统中不同粒子间的纠缠，在系统尺寸趋于无穷大的热力学极限下存在多粒子纠缠。这种宏观纠缠，因为它可以表现出奇异的行为，能够跟踪量子相变。本文对横向磁场中的一维伊辛模型的上下自旋纠缠进行了解析计算。随着耦合强度的变化，纠缠的一阶导数出现跳跃不连续，二阶导数在量子临界点附近发散。
Asymptotic equipartition property of subadditive multipartite entanglement measures on pure states
本文针对纯态上的次可加多体纠缠度量，构建了渐近等分性质，证明光滑弱可加度量的正则化产生弱可加且渐近连续的度量，并表明Rényi型度量的正则化归结为双体纠缠熵的凸组合。
The theoretical method to study strong coupling between an ensemble of quantum emitters (QEs) and surface plasmons excited by the nanoparticle cluster has been presented by using a rigorous first-principles electromagnetic Green's tensor technique. We have demonstrated that multi-qubit entanglement for two-level QEs can be produced at different frequencies simultaneously, when they locate in hot spots of metallic nanoparticle clusters. The duration of quantum beats for such an entanglement can reach two orders longer than that for the entanglement in a photonic cavity. The phenomenon originate…
Time Evolution of Multi-Party Entanglement Signals
研究混沌量子多体系统中多 parties 纠缠信号的时间演化，揭示其丰富的结构特征及动态相变现象。
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