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The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Xiaochun Mei

Quantum technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability of…

Quantum Physics · Physics 2015-12-04 Sai Vinjanampathy , Kavan Modi

Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting…

Quantum Physics · Physics 2011-10-04 Wojciech Roga

We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between…

Quantum Physics · Physics 2019-12-10 Wallas S. Nascimento , Marcos M. de Almeida , Frederico V. Prudente

Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts…

Quantum Physics · Physics 2022-03-14 Boaz Tamir , Ismael L. Paiva , Zohar Schwartzman-Nowik , Eliahu Cohen

We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality case for the monotonicity of relative…

Quantum Physics · Physics 2007-05-23 Patrick Hayden , Richard Jozsa , Denes Petz , Andreas Winter

Quantum information theory, particularly its entropic formulations, has made remarkable strides in characterizing quantum systems and tasks. However, a critical dimension remains underexplored: computational efficiency. While classical…

Quantum Physics · Physics 2026-05-05 Noam Avidan , Thomas A. Hahn , Joseph M. Renes , Rotem Arnon

We approach the physical implications of the non-commutative nature of Complementary Observable Algebras (COA) from an information theoretic perspective. In particular, we derive a general \textit{entropic certainty principle} stating that…

High Energy Physics - Theory · Physics 2021-01-20 Javier M. Magan , Diego Pontello

Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…

General Physics · Physics 2024-10-21 Daegene Song

We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to…

Quantum Physics · Physics 2007-05-23 Benjamin Schumacher , Michael D. Westmoreland

We consider universal methods for obtaining (uniform) continuity bounds for characteristics of multipartite quantum systems. We pay a special attention to infinite-dimensional multipartite quantum systems under the energy constraints. By…

Quantum Physics · Physics 2021-09-28 M. E. Shirokov

We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible…

Quantum Physics · Physics 2016-09-06 Andreas Winter

In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems and we introduce the notion of coefficient of quantum correlations. Our presentation stems from rigorous…

Mathematical Physics · Physics 2016-09-07 W A Majewski

A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…

Quantum Physics · Physics 2009-10-28 N. J. Cerf , C. Adami

We put forth a unifying formalism for the description of the thermodynamics of continuously monitored systems, where measurements are only performed on the environment connected to a system. We show, in particular, that the conditional and…

Quantum Physics · Physics 2022-09-13 Gabriel T. Landi , Mauro Paternostro , Alessio Belenchia

We review the fundamental properties of the quantum relative entropy for finite-dimensional Hilbert spaces. In particular, we focus on several inequalities that are related to the second law of thermodynamics, where the positivity and the…

Statistical Mechanics · Physics 2023-04-18 Takahiro Sagawa

In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…

Chaotic Dynamics · Physics 2015-03-10 Valentina A. Unakafova , Anton M. Unakafov , Karsten Keller

We introduce the notions of returns, dispersions and well-aligned sets for closed relations on compact metric spaces and then we use them to obtain non-trivial sufficient conditions for such a relation to have non-zero entropy. In addition,…

Dynamical Systems · Mathematics 2022-10-06 Iztok Banic , Rene Gril Rogina , Judy Kennedy , Van Nall

Through the generalization of Khinchin's classical axiomatic foundation, a basis is developed for nonadditive information theory. The classical nonadditive conditional entropy indexed by the positive parameter q is introduced and then…

Quantum Physics · Physics 2009-11-07 Sumiyoshi Abe

We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum…

Quantum Physics · Physics 2026-04-13 Giovanni Chesi , Lorenzo Maccone