Related papers: Properties of subentropy
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the…
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately it has emerged that they are in fact intimately related. In this…
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…
We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold.…
In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the…
We define a quantum entropy conditioned on post-selection which has the von Neumann entropy of pure states as a special case. This conditional entropy can take negative values which is consistent with part of a quantum system containing…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…
The von Neumann entropy of a quantum state is a central concept in physics and information theory, having a number of compelling physical interpretations. There is a certain perspective that the most fundamental notion in quantum mechanics…
This paper is devoted to systematic study of properties of the quantum entropy and of the Holevo capacity considered as a function of a set of quantum states. The properties of restriction of the quantum entropy to arbitrary set of states…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$…
We show how the fundamental entropic inequality proved recently in [arXiv:2408.15306] can be applied to obtain a useful relation for the Holevo quantity of discrete and continuous ensembles of quantum states. This relation gives a tight…
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…
General quantum measurements are represented by instruments. In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a…
In this paper a general definition of quantum conditional entropy for infinite-dimensional systems is given based on recent work of Holevo and Shirokov arXiv:1004.2495 devoted to quantum mutual and coherent informations in the…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…