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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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TL;DR: In this article, an introductory study about entropy and its properties and its role in quantum information theory is presented, and the authors use these results to the analysis of a quantum game described by a density operator and with its entropy equal to von Neumann's.
Abstract: The present work is an introductory study about entropy its properties and its role in quantum information theory. In a next work, we will use these results to the analysis of a quantum game described by a density operator and with its entropy equal to von Neumann's.
5 citations
TL;DR: In this article, the authors analyze the quantum capacity from the perspective of algorithmic complexity and show that quantum capacity based on semi-computable concept equals the entropy rate of coherent information, which in turn equals the standard quantum capacity.
Abstract: We analyze the notion of quantum capacity from the perspective of algorithmic (descriptive) complexity. To this end, we resort to the concept of semi-computability in order to describe quantum states and quantum channel maps. We introduce algorithmic entropies (like algorithmic quantum coherent information) and derive relevant properties for them. Then we show that quantum capacity based on semi-computable concept equals the entropy rate of algorithmic coherent information, which in turn equals the standard quantum capacity. Thanks to this, we finally prove that the quantum capacity, for a given semi-computable channel, is limit computable.
5 citations
TL;DR: A maximizer for the quantum mutual information for classical information sent over the quantum amplitude damping channel is obtained by limiting the ensemble of input states to antipodal states, in the calculation of the product state capacity for the channel.
Abstract: We obtain a maximizer for the quantum mutual information for classical information sent over the quantum amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product state capacity for the channel. We also consider the product state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels.
5 citations
TL;DR: In this article, the fundamental properties of the quantum f-relative entropy, where f(.) is an operator convex function, were studied and the equality conditions under monotonicity and joint convexity were given.
Abstract: We study the fundamental properties of the quantum f-relative entropy, where f(.) is an operator convex function. We give the equality conditions under monotonicity and joint convexity, and these conditions are more general than, since they hold for a class of operator convex functions, and different for f(t) = -ln(t) from, the previously known conditions. The quantum f-entropy is defined in terms of the quantum f-relative entropy and we study its properties giving the equality conditions in some cases. We then show that the f-generalizations of the Holevo information, the entanglement-assisted capacity, and the coherent information also satisfy the data processing inequality, and give the equality conditions for the f-coherent information.
5 citations
TL;DR: An approach to self-organizing systems based upon information theory is presented and it is shown that the capacity of an information source is given by the logarithm of its inverse entropy rather than by its negative entropy.
Abstract: This paper is the continuation of a preceding one which appeared in this journal, and presented an approach to self-organizing systems based upon information theory. To begin with, some illustrating examples try to show why one can think that the concept of information should play a crucial role in a theory of general systems. Then the concept of ‘ structural entropy ’, and the ‘ evolution principle ’ that we have previously introduced, are improved here in a definitive form. The concept of ‘ information potential ’ is defined and we show that the capacity of an information source is given by the logarithm of its inverse entropy rather than by its negative entropy. Composition laws for the structural entropy are stated and it is shown that these concepts provide an approach to information balance. Some simple examples are outlined to connect this approach with well known existing results.
5 citations