Grigori Amosov
We study mixed unitary quantum channels generated by irreducible projective unitary representations of finite groups. Under some assumptions on the probability distribution determining a mixture the classical capacity of the channel is found. Examples illustrating the techniques are given.
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
We give a pedagogical presentation of the irreducible unitary representations of $\mathbb{C}^4\rtimes\mathbf{Spin}(4,\mathbb{C})$, that is, of the universal cover of the complexified Poincaré group $\mathbb{C}^4\rtimes\mathbf{SO}(4,\mathbb{C})$. These representations were first investigated by Roffman in 1967. We provide a modern formulation of his results together with some facts from the general Wigner-Mackey theory which are relevant in this context. Moreover, we discuss different ways to realize these representations and, in the case of a non-zero "complex mass", we give a detailed constru…
Explicit constructions of unitary transformations between equivalent irreducible representations
有限群$G$的不可约表示（irreps）是等价的，如果它们之间存在相似变换.在本文中，我们描述了一个显式的算法来构造一对等价的irreps之间的这种变换，假设我们给出了一个算法来计算这些irreps的矩阵元素。在此基础上，我们得到了有限群的非表示的矩阵元的经典正交关系的推广。当我们的群$G$是对称群$S(N)$时，我们给出了共轭Young-Yamanouchi表示的重要情形的酉矩阵的一个显式形式。
Matrix integrals over unitary groups: An application of Schur-Weyl duality
该研究运用Schur-Weyl对偶综述酉群矩阵积分公式，指出其计算与Weingarten函数相关，该函数求值依赖的置换群不可约特征标暂无通用闭式公式，相关信息可通过特征标表获取。
Irreducible Projective Representations and Their Physical Applications
利用本征函数方法约化有限群的正则射影表示，得到其不可约射影表示，并对反酉群进行了特殊处理，引入了解耦因子系和修正的Schur引理.讨论了不可约Reps在多体物理中的应用。结果表明，在对称性保护的拓扑相中，几何缺陷或对称缺陷可以携带对称群的射影Rep;而在对称性丰富的拓扑相中，内禀激发（如自旋子或介子）可以携带对称群的射影Rep.我们还讨论了投影Reps在与谱简并有关的问题中的应用，例如在量子蒙特卡罗模拟中寻找无符号模型的问题。
Hitting time expressions for quantum channels: beyond the irreducible case and applications to unitary walks
本文利用广义逆研究有限维量子信道中粒子到达目标子空间的平均中靶时间，将方法从不可约情形推广到可约情形及任意到达子空间，并应用于酉量子行走。
The paraboson Fock space and unitary irreducible representations of the Lie superalgebra osp(1|2n)
已知正交辛李超代数osp（1）的定义关系|2n）等价于n对抛物算子$b^\pm_i$的定义（三元）关系.特别地，在通常的星条件下，这意味着“p阶抛物子"对应于osp（1）的酉不可约（无限维）最低权表示V（p| 2n）。除了简单的情况p=1或n=1，这些表示从来没有被构造由于计算困难，尽管他们的重要性。在本文中，我们给出了这些表示V（p）的一个明确而优美的构造，并给出了osp（1）的明确作用或矩阵元素|2n）发电机。V（p）的正交基向量用Gelfand-Zetlin模式表示，其中osp（1）的子代数u（n|（2）起着关键作用。我们的结果还导出了这些无穷维OSP（1）的特征公式|2n）陈述。进一步考虑分支$ osp(1|2n) \supset sp(2n) \supset u(n)$，我们得到了sp（2n）的显式无穷维酉不可约最低权表示及其特征标.
Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0> in space without interference, instead of two coin states |1>, |0> .For the case of no boundary conditions, the model is similar to a Markov chain with a stochastic matrix, i.e., it conserves the population distribution of the four coin states, and by using a proper transformation, yield probability distributions of the two quantum states |1>, |0> in space,…
Dual-unitary circuits have emerged as a minimal model for chaotic quantum many-body dynamics in which the dynamics of correlations and entanglement remains tractable. Simultaneously, there has been intense interest in the effect of measurements on the dynamics of quantum information in many-body systems. In this work we introduce a class of models combining dual-unitary circuits with particular projective measurements that allow the exact computation of dynamical correlations of local observables, entanglement growth, and steady-state entanglement. We identify a symmetry preventing a measureme…
We classify the Markov chains that can be generated on the set of quantum states by a unitarily evolving 3-dim quantum system (qutrit) that is repeatedly measured with a projective measurement (PVM) consisting of one rank-2 projection and one rank-1 projection. The dynamics of such a system can be visualized as taking place on the union of a Bloch ball and a single point, which correspond to the respective projections. The classification is given in terms of the eigenvalues of the 2x2 matrix that describes the dynamics arising on the Bloch ball, i.e., on the 2-dim subsystem. We also express th…
GroupFunctions.jl: computing individual entries of the irreducible representations of the unitary group U(d)
研究利用Julia库GroupFunctions.jl计算酉群U(d)不可约表示的单个矩阵元素，通过盖尔范德-采特林模式在载体空间基中计算，还具备多种功能，可导出与Mathematica兼容的结果。
Bounds in the Projective Unitary Group with Respect to Global Phase Invariant Metric
本文研究了在全局相位不变度量下项目性酉群的界限，推导了Gilbert-Varshamov和Hamming界限，并探讨了码本的最小距离、失真率和覆盖半径等特性。
Universal quantum computation using only projective measurement, quantum memory, and preparation of the 0 state
什么资源是量子计算的通用资源？在标准模型中，量子计算机由一系列酉门组成，这些酉门相干地作用于构成计算机的量子比特。这篇论文表明，一个非常不同的模型，只涉及投影测量，量子存储器，以及准备的能力，|0>态对于量子计算也是普适的。特别是，计算中不涉及相干么正动力学。
Fast quantum algorithms for approximating some irreducible representations of groups
我们考虑估计群的酉不可约表示的矩阵元素的量子复杂性。对于几个有限群，包括对称群，量子傅里叶变换产生有效的解决方案，这个问题。此外，量子舒尔变换产生有效的解决方案，某些不可约表示的酉群。除此之外，我们还得到了由交错群A_n的所有不可约表示，以及U（n），SU（n）和SO（n）的多项式最高权的所有不可约表示来逼近矩阵元的poly（n）-时间量子算法.这些量子算法在最坏情况下的复杂度比已知最快的经典算法提供指数加速。另一方面，我们表明，平均情况下的实例是经典的容易，这里分析的技术不提供一个加速超过经典的计算组字符的估计。
Quantum Codes and Irreducible Products of Characters
该研究定义扭酉1-群并证明其对应特征标不可约乘积，将量子码构造转化为有限群特征标计算，结合GAP与文献结果发现了多种带特殊横向门的新型非平凡量子码。
Robust self-test of the maximally entangled state of two-qubits without assuming unitary observables
研究不假设酉可观测量的两量子比特最大纠缠态的稳健自测试问题，通过规避测量装置的扩张，对物理非投影算子进行正则化并得出解析稳健性界限。
Witnessing random unitary and projective quantum channels: Complementarity between separable and maximally entangled states
量子计算和量子通信的现代应用要求精确表征量子态和量子信道。在实践中，这意味着人们必须根据可测量的量来确定物理系统的量子容量。证人，如果适当地构建，成功地执行这一任务。我们推导出一种方法，能够计算证人确定性的演变和测量引起的崩溃过程。同时，利用Choi-Jamiolkowski同构，揭示了二体量子态的纠缠特性。值得注意的是，幺正演化的统计混合映射到最大纠缠态的混合上，而经典的可分态起源于真正的量子态约简映射。基于我们的处理，我们能够一次见证这些相反的属性，并且进一步洞察它们不同的几何结构。的互补性进一步得到了支持，制定一个互补的施密特分解的最大纠缠态和离散傅立叶变换施密特系数的状态。
Starting from a state of low quantum entanglement, local unitary time evolution increases the entanglement of a quantum many-body system. In contrast, local projective measurements disentangle degrees of freedom and decrease entanglement. We study the interplay of these competing tendencies by considering time evolution combining both unitary and projective dynamics. We begin by constructing a toy model of Bell pair dynamics which demonstrates that measurements can keep a system in a state of low (i.e. area law) entanglement, in contrast with the volume law entanglement produced by generic pur…
On some projective unitary qutrit gates
作为协议的一部分，我们在$4$水平上以一定的方式编织了$SU(2)$的Kauffman-Jones版本的Chern-Simons理论中的六个拓扑荷$222211$的任意子。我们得到的门是一个辫子通常qutrit $2222$，但相对于不同的基础。关于该基础，\cite{LEV}的Freedman群与$D$ -群$D(18,1,1;2,1,1)$相同。我们给出了$D(18,1,1;2,1,1)$群的每个Blichfeld生成元的物理解释。受这些用于qutrit的新技术的启发，我们能够为量子位$1221$制造新的附属物，即$\frac{1}{\sqrt{2}}(|1>\,+|3>)$和$\frac{1}{\sqrt{2}}(|1>\,-|3>)$。
We investigate entanglement of purification in conformal field theory. By using Reeh-Schlieder theorem, we construct a set of the purification states for $ρ_{AB}$, where $ρ_{AB}$ is reduced density matrix for subregion $AB$ of a global state $ρ$. The set can be approximated by acting all the unitary observables,located in the complement of subregion $AB$, on the global state $ρ$, as long as the global state $ρ$ is \text{cyclic} for every local algebra, e.g., the vacuum state. Combining with the gravity explanation of unitary operations in the context of the so-called surface/state corresponden…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。