Strong converse to the quantum channel coding theorem
Tomohiro Ogawa,Hiroshi Nagaoka +1 more
TLDR
A lower bound on the probability of decoding error for a quantum communication channel is presented, from which the strong converse to the quantum channel coding theorem is immediately shown.Abstract:
A lower bound on the probability of decoding error for a quantum communication channel is presented, from which the strong converse to the quantum channel coding theorem is immediately shown. The results and their derivations are mostly straightforward extensions of the classical counterparts which were established by Arimoto (1973), except that more careful treatment is necessary here due to the noncommutativity of operators.read more
Citations
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Quantum Information Theory
TL;DR: The author develops all of the tools necessary for understanding important results in quantum information theory, including capacity theorems for classical, entanglement-assisted, private and quantum communication.
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Strong converse for identification via quantum channels
Rudolf Ahlswede,Andreas Winter +1 more
TL;DR: In this article, the authors present a simple proof of the strong converse for identification via discrete memoryless quantum channels, based on a novel covering lemma, which involves a development of explicit large deviation estimates to the case of random variables taking values in self-adjoint operators on a Hilbert space.
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Coding theorem and strong converse for quantum channels
TL;DR: A new proof of Holevo's (1973, 1977) coding theorem for transmitting classical information through quantum channels, and its strong converse is presented, largely inspired by Wolfwitz's combinatorial approach using types of sequences.
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Evaluating capacities of bosonic Gaussian channels
TL;DR: In this paper, a general upper bound on the quantum capacity of a one-mode Gaussian channel with attenuation or amplification and classical noise was derived. But the bounds were not explicitly evaluated for the case of a single-mode channel.
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Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy
TL;DR: In this paper, the authors show that strong converse theorem holds for the classical capacity of all entanglement-breaking channels and all Hadamard channels (the complementary channels of the former), and bounding the success probability in terms of a "sandwiched" Renyi relative entropy.
References
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Optimization by Vector Space Methods
TL;DR: This book shows engineers how to use optimization theory to solve complex problems with a minimum of mathematics and unifies the large field of optimization with a few geometric principles.
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Probabilistic and Statistical Aspects of Quantum Theory
TL;DR: In this article, the authors present a statistical model of quantum theory, including symmetry groups in quantum mechanics, and unbiased measurement and optimality of Gaussian states, and supplement - Statistical Structure of Quantum Theory and Hidden Variables.
Book
Probabilistic and statistical aspects of quantum theory
TL;DR: In this paper, the authors present a statistical model of quantum theory, including symmetry groups in quantum mechanics, and unbiased measurement and optimality of Gaussian states, and supplement - Statistical Structure of Quantum Theory and Hidden Variables.
Book
Quantum Entropy and Its Use
雅則 大矢,Dénes Petz +1 more
TL;DR: In this article, the authors introduce fundamental concepts for Entropies for Finite Quantum Systems and postulates for Entropy and Relative Entropy for General Quantum Systems, as well as Modular Theory and Auxiliaries.