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Coherent information

About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.


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Proceedings ArticleDOI
17 Feb 2015
TL;DR: The third definition of entropy of distribution P, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy.
Abstract: Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information.

6 citations

Posted Content
TL;DR: In the information interpretation of quantum mechanics, information is the most fundamental, basic entity and the concept of a many-to-one state reduction is not a fundamental one but results from the practical impossibility to reconstruct the original state after the measurement.
Abstract: In the information interpretation of quantum mechanics, information is the most fundamental, basic entity. Every quantized system is associated with a definite discrete amount of information (cf. Zeilinger). This information content remains constant at all times and is permutated one-to-one throughout the system evolution. What is interpreted as measurement is a particular type of information transfer over a fictitious interface. The concept of a many-to-one state reduction is not a fundamental one but results from the practical impossibility to reconstruct the original state after the measurement.

6 citations

Proceedings ArticleDOI
01 Dec 2015
TL;DR: This tutorial session aims to describe the key elements of certain non-probabilistic entropy and information concepts for state estimation and control, based on a recently developed theory of nonstochastic information.
Abstract: Entropy and information are crucial notions in stochastic communication systems. However, they have arguably not been as central in control theory, which has a rich tradition of non-random models and techniques. This tutorial session aims to describe the key elements of certain non-probabilistic entropy and information concepts for state estimation and control. In this paper, which comprises the first half of the session, the focus is on a recently developed theory of nonstochastic information. Motivated by worst-case estimation and control, this framework allows non-statistical analogues of mutual independence, Markovness, information, and directed information to be rigorously defined. This yields powerful information-theoretic tools for finding fundamental bounds in zero-error communication and worst-case control systems. In the second half of this session, notions of entropy for deterministic nonlinear control systems are described, based on dynamical systems theory. These notions lead to characterisations of minimal feedback data rates for set-invariance. Taken together, the concepts discussed in this session give deterministic control theorists a way to use information and entropy ideas, without having to adopt a stochastic formulation.

6 citations

Proceedings ArticleDOI
L.B. Levitin1
02 Oct 1992
TL;DR: A short review of the development of the physical information theory is presented and BrillouinS conjecture of minimum enerrgy per unit of information is proved for this type of channels.
Abstract: A short review of the development of the physical information theory is presented. The entropy defect principle is formulated for quasiclassical systems. The concept of ideal physical information channels is iintroduced. It is shown that information properties of such a channel with independent additive noise can be ontained from the thermodynamic description of the physical system that transmits information. BrillouinS conjecture of minimum enerrgy per unit of information is proved for this type of channels.

6 citations

Journal ArticleDOI
TL;DR: This work defines an optimal decomposition as a decomposition for which the average preparation information is minimal, and characterizes the system–environment correlations.
Abstract: Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition. We then define an optimal decomposition as a decomposition for which the average preparation information is minimal. The average preparation information for an optimal decomposition characterizes the system-environment correlations. We discuss properties and applications of the concepts introduced above and give several examples.

6 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20234
202211
202122
202017
201923
201818