Eli Eisenberg, Larry Horwitz
It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively pure state can evolve under the usual unitary evolution to an effectively mixed state.
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We introduce ways to measure information storage in quantum systems, using a recently introduced computation-theoretic model that accounts for measurement effects. The first, the quantum excess entropy, quantifies the shared information between a quantum process's past and its future. The second, the quantum transient information, determines the difficulty with which an observer comes to know the internal state of a quantum process through measurements. We contrast these with von Neumann entropy and quantum entropy rate and provide a closed-form expression for the latter for the class of deter…
Maximal intrinsic randomness of a quantum state
该研究针对量子态内禀随机性提取量的基础问题，分别给出条件最小熵、条件冯·诺依曼熵和条件最大熵三种度量下的最大值及对应的最优测量方式，填补了相关研究空白。
We consider free fermion systems in arbitrary dimensions and represent the occupation pattern of each eigenstate as a classical binary string. We find that the Kolmogorov complexity of the string correctly captures the scaling behavior of its entanglement entropy (EE). In particular, the logarithmically-enhanced area law for EE in the ground state and the volume law for EE in typical highly excited states are reproduced. Since our approach does not require bipartitioning the system, it allows us to distinguish typical and atypical eigenstates directly by their intrinsic complexity. We reveal t…
We study the temporal rate of variations of the von Neumann entropy in an open quantum system which interacts with a bath. We show that for almost all initial states of the bath and the system, the time-average of the rate of entropy change is bounded by a function which depends on various properties of the system and environment, and is mostly relatively small. This result holds true under fairly general conditions in almost any arbitrary quantum system.
The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate interpretations of coherence measures and the interplay with other quantum properties, such as quantum correlations and intrinsic randomness. Coherence can be viewed as the resource for the intrinsic randomness in the measurement outcomes of a state in the computational basis. We observed in our previous work that the coherence of formation, which measures the …
Inequality for von Neumann entropy change under measurement and dissipation
该研究推导连续测量与耗散下系综平均冯·诺依曼熵变的普适下界，纳入非厄米耗散、测量涨落及非对易量子方差，并将经典信息热力学关系推广至量子领域。
The leakage chain rule for quantum min-entropy quantifies the change of min-entropy when one party gets additional leakage about the information source. Herein we provide an interactive version that quantifies the change of min-entropy between two parties, who share an initial classical-quantum state and are allowed to run a two-party protocol. As an application, we prove new versions of lower bounds on the complexity of quantum communication of classical information.
We present methods for evaluating the rate of change in quantities during quantum evolution due to coupling to the environment (dissipation hereafter). The protocol is based on repeating a given quantum circuit (or quantum operation) twice, thrice, and so on, and measuring an expectation value after each number of repetitions. We start by applying this method for measuring the rate of purity changes in quantum circuits. This provides direct information on the quality of the circuit. Furthermore, the presented scheme enables to distill the dissipative contribution in the changes of quantities s…
The second law of nonequilibrium thermodynamics within the open system paradigm (a small system coupled to one or multiple baths) is derived. This is done by showing positivity of entropy production for arbitrary Hamiltonian dynamics for a large class of initial states. Using the recently introduced notion of observational entropy, shortcomings of previous approaches are overcome. I apologize that the actual abstract of the manuscript is longer than the arXiv guidelines allow and therefore not displayed here.
Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, as different fro…
It is well known in the realm of quantum mechanics and information theory that the entropy is non-decreasing for the class of unital physical processes. However, in general, the entropy does not exhibit monotonic behavior. This has restricted the use of entropy change in characterizing evolution processes. Recently, a lower bound on the entropy change was provided in the work of Buscemi, Das, and Wilde~[Phys.~Rev.~A~93(6),~062314~(2016)]. We explore the limit that this bound places on the physical evolution of a quantum system and discuss how these limits can be used as witnesses to characteri…
Quantum Energy Teleportation and Entropy Change due to Feedback Control in One-Dimensional Heisenberg Model
本研究针对四自旋一维海森堡模型，通过调控边缘局域磁场改变基态纠缠，结合投影测量与依赖测量结果的反馈控制实现量子能量隐形传态，发现提取能量在磁场中间值达最大且与反馈熵变近似成正比，并从纠缠热力学角度解释了反馈控制的作用。
Entropy dynamics for a harmonic propeller-shaped planar molecular quantum Brownian rotator
本文以熵相对变化度量谐波场中分子齿轮转子的动态稳定性，利用最大熵原理构造初始态，并给出在欠阻尼与非欠阻尼条件下实现低熵变化的态制备与参数条件。
Unifying quantum measurement constructions via a relative-entropy minimum change principle
本文基于相对熵最小变化原理，建立量子统计推断中最优测量的闭式表征，恢复了两类已知测量并发现软最小热测量新家族，还证明该原理的可加性并研究了费米-狄拉克热测量的量子假设检验性能。
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