Subhash Kak
This paper considers quantum communication involving an ensemble of states. Apart from the von Neumann entropy, it considers other measures one of which may be useful in obtaining information about an unknown pure state and another that may be useful in quantum games. It is shown that under certain conditions in a two-party quantum game, the receiver of the states can increase the entropy by adding another pure state.
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We present a simple model which allows us to explain the physical nature of the oscillating entropy. We consider an ensemble of qubits interacting with thermal two-level systems. The entropy of the qubits oscillates between zero and the value of entropy of the thermal systems. We show that the oscillations of the entropy can be clearly explained by the precession of the real or effective spins of the qubits.
The Gram matrix of a set of quantum pure states plays key roles in quantum information theory. It has been highlighted that the Gram matrix of a pure-state ensemble can be viewed as a quantum state, and the quantumness of a pure-state ensemble can thus be quantified by the coherence of the Gram matrix [Europhys. Lett. \textbf{134} 30003]. Instead of the $l_1$-norm of coherence and the relative entropy of coherence, we utilize the generalized $α$-$z$-relative Rényi entropy of coherence of the Gram matrix to quantify the quantumness of a pure-state ensemble and explore its properties. We show th…
We consider a scheme of multiplexed cold atomic ensembles that generate a frequency-entangled biphoton state with controllable entropy of entanglement. The biphoton state consists of a telecommunication photon (signal) immediately followed by an infrared one (idler) via four-wave mixing with two classical pump fields. Multiplexing the atomic ensembles with frequency and phase-shifted signal and idler emissions, we can manipulate and control the spectral property of the biphoton state. Mapping out the entropy of entanglement in the scheme provides the optimal configuration for entanglement reso…
A note on continuous ensemble expansions of quantum states
推广了相对熵的概念，给出了量子系统的先验和后验相对熵的区别。前者称为量子相对熵，与量子态识别有关。后者-一个后验相对量子熵被证明与状态重建由于以下性质：给定一个密度算子$ρ$，系综的纯态与吉布斯分布关于定义的距离被证明代表初始状态$ρ$的白噪声量（完全混合状态），可以任意小。
Distinguishability of States and von Neumann Entropy
考虑一个纯量子态系综|n_j>，j=1，.，n分别取先验概率p_j。我们表明，增加所有的成对重叠是可能的|<_i|联系我们|即，使状态的每个组成对更平行（同时保持先验概率相同），以这样的方式使得冯诺伊曼熵S增加，并且对偶地，使所有对更正交，同时减小S。我们表明，这种现象不会发生在两个维度的合奏，但它是一个功能，几乎所有的合奏三个国家在三个维度。众所周知，冯诺伊曼熵表征了系综的经典和量子信息容量，我们认为，信息容量反过来，是一个信号状态的可扩展性的表现。因此，我们的结果表明，在一个系综的可重复性的概念是一个整体的属性，不能减少到考虑的可重复性的每个组成对的状态。
Entropy-based random quantum states
本文提出基于熵的随机态生成方法，通过构建随机矩阵族并证明其与哈密顿量模型的对偶性，揭示了量子混沌特征。
Volume of classical and quantum ensembles: geometric approach to entropy and information
它示出的经典和量子系综，有一个独特的量，具有“体积”的属性。这个量是系综熵的函数，因此为后者提供了几何解释。它进一步提供了一个几何图片推导和统一的结果，在经典和量子信息理论，并讨论熵的不确定性关系。
Quantification of quantum correlation of ensemble of states
我们提出了第一个测量的量子关联的合奏的多方状态。它是基于局部可区分基测量中的最小熵产生的思想。它被证明是一个相对熵距离从一组合奏。对于跨越整个二分希尔伯特空间的二分系综，该测度被纠缠的平均相对熵所限制。我们自然地得到了一个单调性公理的任何措施的量子相关系综。我们在某些情况下评估这一措施。随后，我们使用这个措施，提出了我们的措施和可获得的信息之间的互补关系的合奏下的本地操作。即使对于单个系统的情况，该度量和单调性公理也是明确定义的，其中互补关系被视为“海森堡不确定关系”的另一个方面。
Information, Relative Entropy of Entanglement and Irreversibility
先前提出的纠缠度，如纠缠的形成和援助，被证明是特殊情况下的相对熵的纠缠。这些措施的混合状态的合奏之间的差异示出依赖于特定成员的合奏的经典信息的可用性。在此基础上，导出了纠缠的相对熵与互信息的关系。
Effect of initial intrasystem entanglement on entropy growth in generalized Jaynes-Cummings models
研究初始系统纠缠对广义Jaynes-Cummings模型中熵增长的影响，发现初始纠缠与熵增长正相关，且集合平均行为显示不同贡献。
The entropy of the Gram matrix of a joint purification of an ensemble of K mixed states yields an upper bound for the Holevo information Chi of the ensemble. In this work we combine geometrical and probabilistic aspects of the ensemble in order to obtain useful bounds for Chi. This is done by constructing various correlation matrices involving fidelities between every pair of states from the ensemble. For K=3 quantum states we design a matrix of root fidelities that is positive and the entropy of which is conjectured to upper bound Chi. Slightly weaker bounds are established for arbitrary ense…
Microscopic Legendre Transform, Canonical Ensemble and Jaynes' Maximum Entropy Principle
本文提出自由能与香农熵之间的微观勒让德变换，以微观态概率和缩放能量为共轭变量，利用香农熵的精确微分性质推导正则系综核心关系，并与Jaynes最大熵原理比较，为信息熵与热力学熵的联系提供新视角。
The Sachdev-Ye-Kitaev model is an $N$-modes fermionic model with infinite range random interactions. In this work, we study the thermal Rényi entropy for a subsystem of the SYK model using the path-integral formalism in the large-$N$ limit. The results are consistent with exact diagonalization [1] and can be well approximated by thermal entropy with an effective temperature [2] when subsystem size $M\leq N/2$. We also consider generalizations of the SYK model with quadratic random hopping term or $U(1)$ charge conservation.
Average entropy of Bogoliubov-Kubo-Mori random state ensemble
研究基于Bogoliubov-Kubo-Mori度量的随机态系综，推导出平均纠缠熵的精确显式公式，为计算高阶累积量奠定基础。
Hybrid quantum-classical systems: statistics, entropy, microcanonical ensemble and its connection to the canonical ensemble
本文提出了一种数学框架，用于描述混合量子-经典系统的统计集合，并通过最大熵原理推导微正则集，探讨其与正则集的关系及混合系统的量子化特性。
Average entanglement entropy of a small subsystem in a constrained pure Gaussian state ensemble
研究通过高斯态集合分析小子系统平均纠缠熵，发现其与无关联混合高斯态的von Neumann熵相同，并探讨其在霍金辐射模型中的应用。
In order to find out for which initial states of the system the uncertainty of the measurement outcomes will be minimal, one can look for the minimizers of the Shannon entropy of the measurement. In case of group covariant measurements this question becomes closely related to the problem how informative the measurement is in the sense of its informational power. Namely, the orbit under group action of the entropy minimizer corresponds to a maximally informative ensemble of equiprobable elements. We give a characterization of such ensembles for 3-dimensional group covariant (Weyl-Heisenberg) SI…
Between entropy and subentropy
混合量子态的冯诺伊曼熵和子熵分别是与给定混合态一致的任何系综的可达信息的上界和下界。在这里，我们定义和研究一组介于熵和亚熵之间的量。
Entanglement entropy is a powerful tool in characterizing universal features in quantum many-body systems. In quantum chaotic Hermitian systems, typical eigenstates have near maximal entanglement with very small fluctuations. Here, we show that for Hamiltonians displaying non-Hermitian many-body quantum chaos, modeled by the Ginibre ensemble, the entanglement entropy of typical eigenstates is greatly suppressed. The entropy does not grow with the Hilbert space dimension for sufficiently large systems and the fluctuations are of equal order. We derive the novel entanglement spectrum that has in…
Ensemble dependence of information-theoretic contributions to the entropy production
研究开放系统熵产生的信息论贡献对系综的依赖性，发现不同环境统计系综在产生相同总熵产生时，其互信息与位移项的相对权重取决于储层初始状态。
Universal geometric approach to uncertainty, entropy and information
结果表明，对于任何合奏，无论是经典的或量子的，连续的或离散的，只有一个措施的“体积”的合奏，是兼容的几个基本几何假设。因此，该体积测量是用于表征集合的固有扩散、分散、定位等的优选和通用选择。值得注意的是，这个独特的“系综体积”是一个简单的函数的系综熵，因此提供了一个新的几何表征后者的数量。应用包括统一的，基于体积的推导的Holevo和香农界限在量子和经典信息理论;一个精确的几何解释热力学熵的平衡系综;几何推导的半经典不确定性关系;一个新的手段定义经典和量子局域化的任意演化过程;几何解释的相对熵;以及一种新提出的光束光斑尺寸的定义。的合奏体积比其他本地化措施（均方根偏差，Renyi熵，和逆参与比）的优势进行了讨论。
The von Neumann entropy and information rate for ideal quantum Gibbs ensembles
基于理想（自由）粒子（玻色子或费米子）的吉布斯系综，提出了一个量子信息源模型。我们确定（热力学）冯诺伊曼熵的信息率，并建立经典的Lempel-Ziv通用编码算法在Grassberger的形式，这样的源。这将舒马赫定理推广到非IID量子比特的情况。
Spectral moments of Bures-Hall ensemble and applications to entanglement entropy
本文研究了Bures-Hall随机矩阵的谱矩，推导出适用于实数k的递推关系，并应用于重新推导Bures-Hall集合的平均冯·诺依曼熵和量子纯度公式。
We derived the equation of the density operator for generalized entropy and generalized expectation value with quantum analysis when conserved quantities exist. The derived equation is simplified when the conventional expectation value is employed. The derived equation is also simplified when the commutation relations, $[\hatρ, \hat{H}]$ and $[\hatρ, \hat{Q}^{[a]}]$, are the functions of the density operator $\hatρ$, where $\hat{H}$ is the Hamiltonian, and $\hat{Q}^{[a]}$ is the conserved quantity. We derived the density operators for the von Neumann entropy, the Tsallis entropy, and the Rényi…
Average relative entropy of random states
研究Hilbert-Schmidt和Bures-Hall系综中随机态的平均相对熵，推导出任意维数独立态之间平均相对熵的精确显式公式。
We show that Renyi entropies of subregions can be used to distinguish when the entire system is in a microcanonical ensemble from when it is in a canonical ensemble, at least in theories holographically dual to gravity. Simple expressions are provided for these Renyi entropies in a particular thermodynamic limit with high energy density and fixed fractional size of the subregion. Holographically, the Renyi entropies are determined by the areas of cosmic branes inserted into the bulk spacetime. They differ between a microcanonical and a canonical ensemble because the two ensembles provide diffe…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of these ensembles in statistical descriptions. However, there is still no full consensus on the precise reasoning justifying the use of such ensembles. In this work, we provide a new approach to derive maximum-entropy ensembles taking a strictly operational perspective. We investigate the set of possible transitions that a system can undergo together with an envi…
We consider an ensemble of random density matrices distributed according to the Bures measure. The corresponding joint probability density of eigenvalues is described by the fixed trace Bures-Hall ensemble of random matrices which, in turn, is related to its unrestricted trace counterpart via a Laplace transform. We investigate the spectral statistics of both these ensembles and, in particular, focus on the level density, for which we obtain exact closed-form results involving Pfaffians. In the fixed trace case, the level density expression is used to obtain an exact result for the average Hav…
On average output entropy of a quantum channel
该研究分析量子信道平均输出熵的解析性质，推导其在秩/能量约束下的紧半连续界，给出Holevo信息新界、改进形成纠缠界，并提出广义系综新度量与无源能量概念。
Subsystem entropy in 2d CFT and KdV ETH
本文研究二维共形场论中子系统熵，通过比较初级态与KdV系综，证明结果符合KdV广义子系统本征态热化假说，解决了初级态与热态纠缠谱行为表面矛盾的问题。
Maximum Geometric Quantum Entropy
本文提出最大几何量子熵原理，利用量子信息维度和几何量子熵概念，从无限多个纯态系综中唯一选择熵最大的一个，并给出解析解及物理机制解释。
The Bures-Hall distance metric between quantum states is a unique measure that satisfies various useful properties for quantum information processing. In this work, we study the statistical behavior of quantum entanglement over the Bures-Hall ensemble as measured by von Neumann entropy. The average von Neumann entropy over such an ensemble has been recently obtained, whereas the main result of this work is an explicit expression of the corresponding variance that specifies the fluctuation around its average. The starting point of the calculations is the connection between correlation functions…
In the context of non-relativistic quantum mechanics, we investigated Shannon's entropy of a non-Hermitian system to understand how this quantity is modified with the cyclotron frequency. Subsequently, we turn our attention to the construction of an ensemble of these spinless particles in the presence of a uniform magnetic field. Then, we study the thermodynamic properties of the model. Finally, we show how Shannon's entropy and thermodynamic properties are modified with the action of the magnetic field.
Do mixed states exhibit deep thermalisation?
研究混合态是否能深度热化，引入针对混合态的深度热化新范式，通过从扩展系统最大熵系综追踪辅助自由度产生系综，在局部相互作用混沌系统中证明其动态出现，对自对偶踢伊辛链得出有限时间内精确出现该系综的结果，为相关动力学提供见解。
Typical Positivity of Nonequilibrium Entropy Production for Pure States
本文证明在有效维度足够大时，大多数纯态的非平衡动力学产生与系综相同的熵，从而确立熵产生的正性，并补充了纯态第二定律的研究。
A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
本文提出最大熵原理统一刻画希尔伯特空间遍历性与深度热化中的纯态系综，推导统计矩公式并数值验证其普适性，同时揭示其信息论含义。
We propose a generalization of the quantum entropy introduced by Wigner and von Neumann in 1929 [Zeitschrift für Physik 57, 30 (1929)]. Our generalization is applicable to both quantum pure states and mixed states. When the dimension $N$ of the Hilbert space is large, as a result of typicality, this generalized Wigner-von Neumann (GWvN) entropy becomes independent of choices of basis and is asymptotically equal to $\ln N$. The dynamic evolution of our entropy is also typical, reminiscent of quantum H theorem proved by von Neumann. For the microcanonical ensemble, the GWvN entropy is equivalent…
Motivated by the anisotropic long-range nature of the interactions between cold dipolar atoms or molecules in an optical lattice, we study the anisotropic quantum Heisenberg model with Curie-Weiss-type long-range interactions. Absence of a heat bath in optical lattice experiments suggests a study of this model within the microcanonical ensemble. The microcanonical entropy is calculated analytically, and nonequivalence of microcanonical and canonical ensembles is found for a range of anisotropy parameters. From the shape of the entropy it follows that the Curie-Weiss Heisenberg model is indisti…
It has been argued that gravity acts dissipatively on quantum-mechanical systems, inducing thermal fluctuations that become indistinguishable from quantum fluctuations. This has led some authors to demand that some form of time irreversibility be incorporated into the formalism of quantum mechanics. As a tool towards this goal we propose a thermodynamical approach to quantum mechanics, based on Onsager's classical theory of irreversible processes and on Prigogine's nonunitary transformation theory. An entropy operator replaces the Hamiltonian as the generator of evolution. The canonically conj…
Non-intersecting Squared Bessel Process: Spectral Moments and Dynamical Entanglement Entropy
本文提出基于非相交平方Bessel过程的动态扩展模型，用于计算纠缠度量并研究纠缠熵的动态特性。
Employing one plus two-body random matrix ensembles for bosons, temperature and entropy are calculated, using different definitions, as a function of the two-body interaction strength λfor a system with 10 bosons (m=10) in five single particle levels (N=5). It is found that in a region λ\sim λ_t, different definitions give essentially same values for temperature and entropy, thus defining a thermalization region. Also, (m,N) dependence of λ_t has been derived. It is seen that λ_t is much larger than the λvalues where level fluctuations change from Poisson to GOE and strength functions change f…
In this article we study lossless compression of strings of pure quantum states of indeterminate-length quantum codes which were introduced by Schumacher and Westmoreland. Past work has assumed that the strings of quantum data are prepared to be encoded in an independent and identically distributed way. We introduce the notion of quantum stochastic ensembles, allowing us to consider strings of quantum states prepared in a more general way. For any identically distributed quantum stochastic ensemble we define an associated quantum Markov chain and prove that the optimal average codeword length …
The connection between the non-equilibrium dynamics of isolated quantum many-body systems and statistical mechanics is a fundamental open question. It is generally believed that the unitary quantum evolution of a sufficiently complex system leads to an apparent maximum-entropy state that can be described by thermodynamical ensembles. However, conventional ensembles fail to describe the large class of systems that exhibit non-trivial conserved quantities. Instead, generalized ensembles have been predicted to maximize entropy in these systems. In our experiments we explicitly show that a degener…
Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of th…
We study quantum quenches in the XXZ spin-$1/2$ Heisenberg chain from families of ferromagnetic and antiferromagnetic initial states. Using Bethe ansatz techniques, we compute short-range correlators in the complete generalized Gibbs ensemble (GGE), which takes into account all local and quasi-local conservation laws. We compare our results to exact diagonalization and numerical linked cluster expansion calculations for the diagonal ensemble finding excellent agreement and thus providing a very accurate test for the validity of the complete GGE. Furthermore, we compute the diagonal entropy in …
Skewness of von Neumann entropy over Bures-Hall random states
针对Bures-Hall系综中两体随机态的von Neumann熵分布，本文推导其第三累积量的精确闭式公式以刻画偏度，并借助新的多伽马函数求和恒等式改进分布近似。
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