首页/论文/quant-ph/0601129

arXiv quant-ph/06011292006-01quant-phastro-phcond-mat.stat-mech

Swapping and permutation operators as entanglement witnesses for quantum Heisenberg spin-$s$ systems

Guang-Ming Zhang, Xiaoguang Wang

备注：: 8 pages, no figures, accepted by Journal of Physics A: Mathematical and General
发表信息：: J.Phys. A39 (2006) 8515
DOI：: 10.1088/0305-4470/39/26/017

英文摘要：

Using the SU($N$) representation of the group theory, we derive the general form of the spin swapping operator for the quantum Heisenberg spin-$s$ systems. We further prove that such a spin swapping operator is equal to the spin singlet pairing operator under the partial transposition. For SU(2) invariant states, it is shown that the expectation value of the spin swapping operator and its generalizations, the permutations, can be used as an entanglement witness, especially, for the formulation of observable conditions of entanglement.

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

Non-gaussian Entanglement Swapping between Three-Mode Spontaneous Parametric Down Conversion and Three Qubits

In this work we study the production and swapping of non-gaussian multipartite entanglement in a setup containing a parametric amplifier which generates three photons in different modes coupled to three qubits. We prove that the entanglement generated in this setup is of nongaussian nature. We introduce witnesses of genuine tripartite nongaussian entanglement, valid both for mode and qubit entanglement. Moreover, those witnesses show that the entanglement generated among the photons can be swapped to the qubits, and indeed the qubits display nongaussian genuine tripartite entanglement over a w…

2022-02-04quant-ph

Bell nonlocality and fully-entangled fraction measured in an entanglement-swapping device without quantum state tomography

We demonstrate an efficient experimental procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully-entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. Our method requires neither full quantum stat…

2016-09-30quant-ph

Indecomposability of entanglement witnesses constructed from any permutations

Let $n\geq 2$ and $Φ_{n,t,π}: M_n({\mathbb C}) \rightarrow M_n({\mathbb C})$ be a linear map defined by $Φ_{n,t,π}(A)=(n-t)\sum_{i=1}^nE_{ii}AE_{ii}+t\sum_{i=1}^nE_{i,π(i)}AE_{i,π(i)}^†-A$, where $0\leq t\leq n$, $E_{ij}$s are the matrix units and $π$ is a non-identity permutation of $(1,2,\cdots,n)$. Denote by $\{{ F}_s: s=1,2\ldots, k\}$ the set of all minimal cycles of $π$ and $l(π)=\max\{\# { F}_s: s=1,2,\ldots,k\}$ the length of $π$. It is shown that the Hermitian matrix $W_{n,t,π}$ induced by $Φ_{n,t,π}$ is an indecomposable entanglement witness if and only if $π^2\not={\rm id}$ (the ide…

2014-06-19quant-ph

On swapping the states of two qudits

The SWAP gate has become an integral feature of quantum circuit architectures and is designed to permute the states of two qubits through the use of the well-known controlled-NOT gate. We consider the question of whether a two-qudit quantum circuit composed entirely from instances of the generalised controlled-NOT gate can be constructed to permute the states of two qudits. Arguing via the signature of a permutation, we demonstrate the impossibility of such circuits for dimensions $d \equiv 3$ (mod 4).

2011-01-21quant-ph

Optimality of a class of entanglement witnesses for $3\otimes 3$ systems

Let $Φ_{t,π}: M_3({\mathbb C}) \rightarrow M_3({\mathbb C})$ be a linear map defined by $Φ_{t,π}(A)=(3-t)\sum_{i=1}^3E_{ii}AE_{ii}+t\sum_{i=1}^3E_{i,π(i)}AE_{i,π(i)}^†-A$, where $0\leq t\leq 3$ and $π$ is a permutation of $(1,2,3)$. We show that the Hermitian matrix $W_{Φ_{t,π}}$ induced by $Φ_{t,π}$ is an optimal entanglement witness if and only if $t=1$ and $π$ is cyclic.

2013-01-31quant-ph

通过双量子比特见证检测高维态的资源高效纠缠检测

Resource-efficient entanglement detection in high-dimensional states via two-qubit witnesses

本文提出了一种通过双量子比特见证高效检测高维态纠缠的方法，适用于多种状态类型，具有低测量需求和高灵敏度。

2025-09-16quant-ph

更多相关论文收起更多论文

一种使用量子比特与置换的简单量子块建模

A Simple Quantum Blockmodeling with Qubits and Permutations

本文提出一种使用置换矩阵和量子比特测量在量子计算机上解决块建模问题的方法，通过将小规模量子比特测量结果映射为适应度值，在迭代次数小于log(N)时可高效求解。

2024-04-22cs.LGcs.SIquant-ph

含不可区分粒子的量子置换谜题

Quantum permutation puzzles with indistinguishable particles

本文针对置换谜题提出量子版本，将部件替换为不可区分量子粒子，发现单纯置换可映射经典谜题，而添加SWAP平方根量子移动后则无法映射，主要研究2×2滑块谜题量子化并简要探讨2×2×1魔方量子化。

2025-03-14quant-ph

Detection of Genuine Multipartite Entanglement in Quantum Network Scenario

Experimental demonstration of entanglement needs to have a precise control of experimentalist over the system on which the measurements are performed as prescribed by an appropriate entanglement witness. To avoid such trust problem, recently device-independent entanglement witnesses (\emph{DIEW}s) for genuine tripartite entanglement have been proposed where witnesses are capable of testing genuine entanglement without precise description of Hilbert space dimension and measured operators i.e apparatus are treated as black boxes. Here we design a protocol for enhancing the possibility of identif…

2017-01-15quant-ph

Permutation Enhances Classical Communication Assisted by Entangled States

We give a capacity formula for the classical communication over a noisy quantum channel, when local operations and global permutations allowed in the encoding and bipartite states preshared between the sender and the receiver. The two endpoints of this formula are the Holevo capacity (without entanglement assistance) and the entanglement-assisted capacity (with unlimited entanglement assistance). What's more, we show that the capacity satisfies the strong converse property and thus the formula serves as a sharp dividing line between achievable and unachievable rates of communication. We prove …

2020-01-09cs.ITmath.ITquant-ph

Optimization of device-independent witnesses of entanglement depth from two-body correlators

In a recent work [A. Aloy et al. arXiv:1807:06027 (2018)] we have considered the characterization of entanglement depth, from a device-independent perspective, in a quantum many-body system. We have shown that the inequalities introduced in [J. Tura et al. Science 344 1256 (2014)] can be used to obtain device-independent witnesses of entanglement depth and that they enjoy two key properties that allow to compute their $k$-producibility bounds more efficiently for larger system sizes, as well as yielding experimentally-friendlier device-independent witnesses of entanglement depth: they involve …

2019-04-09quant-ph

启发式搜索用于量子APM-LDPC码最小距离上界见证

Heuristic Search for Minimum-Distance Upper-Bound Witnesses in Quantum APM-LDPC Codes

本文研究了通过构造低权非稳定逻辑代表来确定量子APM-LDPC码最小距离上界的方法，利用统一框架和特定结构生成候选，通过排除测试后获得精确上界。

2026-04-16cs.ITmath.ITquant-ph

置换不变贝尔算子的stoquasticity锥的精确半定刻画

An exact semidefinite characterization of the stoquasticity cone of permutationally invariant Bell operators

Universiteit Leiden（莱顿大学）；Instituut-Lorentz, Universiteit Leiden（莱顿大学洛伦兹研究所）；LIACS, Universiteit Leiden（莱顿大学计算科学研究所）

本研究给出置换不变贝尔算子stoquasticity锥在热力学极限下的精确半定刻画，通过单变量多项式将判定转化为单一半定可行性问题，并恢复二体算子的已知结果及三体算子的新边界。

2026-10-05quant-ph

量子计算机中的多体纠缠划分检测

Detection of many-body entanglement partitions in a quantum computer

本文提出基于系统固有对称性、结合弱Schur采样的多体纠缠划分检测方法，可在量子计算机实现，覆盖多类纠缠结构，还推导了相关矩阵不等式新结论。

2025-11-17quant-ph

Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states

We present general numerical methods to construct witness operators for entanglement detection and estimation of the fidelity. Our methods are applied to detecting entanglement in the vicinity of a six-qubit Dicke state with three excitations and also to further entangled symmetric states. All our witnesses are designed to keep the measurement effort small. We present also general results on the efficient local decomposition of permutationally invariant operators, which makes it possible to measure projectors to symmetric states efficiently

2009-08-18quant-ph

Conditional Teleportation of Quantum-Dot Spin States

Among the different platforms for quantum information processing, individual electron spins in semiconductor quantum dots stand out for their long coherence times and potential for scalable fabrication. The past years have witnessed substantial progress in the capabilities of spin qubits. However, coupling between distant electron spins, which is required for quantum error correction, presents a challenge, and this goal remains the focus of intense research. Quantum teleportation is a canonical method to transmit qubit states, but it has not been implemented in quantum-dot spin qubits. Here, w…

2020-06-16cond-mat.mes-hallquant-ph

Positive maps and trace polynomials from the symmetric group

With techniques borrowed from quantum information theory, we develop a method to systematically obtain operator inequalities and identities in several matrix variables. These take the form of trace polynomials: polynomial-like expressions that involve matrix monomials $X_{α_1} \cdots X_{α_r}$ and their traces $\operatorname{tr}(X_{α_1} \cdots X_{α_r})$. Our method rests on translating the action of the symmetric group on tensor product spaces into that of matrix multiplication. As a result, we extend the polarized Cayley-Hamilton identity to an operator inequality on the positive cone, charact…

2020-09-09math-phmath.FAmath.MP

Entanglement-invertible channels（纠缠可逆信道）

Entanglement-invertible channels

本研究推广了Werner的紧约束量子隐形传态与密集编码方案分类，移除维度限制，提出并分类了纠缠可逆信道，证明其等价于量子组合数学中的量子双射，可通过量子置换群表示理论刻画。

2024-06-19math-phmath.MPmath.OA

平均场海森堡模型的戴维斯生成器的谱隙

Spectral Gap of the Davies Generator for the Mean-Field Heisenberg Model

University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；California Institute of Technology（加州理工学院）

研究平均场海森堡模型的戴维斯生成器谱隙，通过比较论证和分解可观测量空间为球张量算符的方法，给出了不同温度下谱隙的渐近估计，揭示了低温下与连续对称性破缺相关的慢化现象。

2026-07-27math-phmath.MPquant-ph