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Quantum Information Processing with Finite Resources: Mathematical Foundations
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This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices, and introduces the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states.Abstract:
This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rnyi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rnyi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.read more
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Quantum Information Theory
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References
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TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
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TL;DR: This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing, with a focus on entanglement.
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TL;DR: Practical application of the generalized Bells theorem in the so-called key distribution process in cryptography is reported, based on the Bohms version of the Einstein-Podolsky-Rosen gedanken experiment andBells theorem is used to test for eavesdropping.
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Possible generalization of Boltzmann-Gibbs statistics
TL;DR: In this paper, a generalized form of entropy was proposed for the Boltzmann-Gibbs statistics with the q→1 limit, and the main properties associated with this entropy were established, particularly those corresponding to the microcanonical and canonical ensembles.
Posted Content
On Information and Sufficiency
TL;DR: The information deviation between any two finite measures cannot be increased by any statistical operations (Markov morphisms) and is invarient if and only if the morphism is sufficient for these two measures as mentioned in this paper.