Quantum information theory

Nature, 2000

This Chapter deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information sheds new light on the conceptual problems of quantum mechanics.

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Some basic facts about QM systems . . . . . . . . . . . . . . . . . . . . . . 2 3 The partial trace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 Classical Shannon entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 Sundry formulas for the Shannon entropy . . . . . . . . . . . . . . . . . . . 4 6 Von Neumann Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 7 Sundry formulas for the Von Neumann entropy . . . . . . . . . . . . . . . . 5 8 H(A) versus S(A)? What is dierent? . . . . . . . . . . . . . . . . . . . . 6 9 Case I (Classical) Independent qubits . . . . . . . . . . . . . . . . . . . . . 6 10 Case II (Classical) Correlated qubits . . . . . . . . . . . . . . . . . . . . . 7 11 Case III (Nonclassical--Purely Quantum Mechanical) Entangled (superc

The aim of this book is to develop "from the ground up" many of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon theory. As such, we spend a significant amount of time on quantum mechanics for quantum information theory (Part II), we give a careful study of the important unit protocols of teleportation, super-dense coding, and entanglement distribution (Part III), and we develop many of the tools necessary for understanding information transmission or compression (Part IV). Parts V and VI are the culmination of this book, where all of the tools developed come into play for understanding many of the important results in quantum Shannon theory.

2000

The paper is intended to be a survey of all the important aspects and results that have shaped the field of quantum computation and quantum information. The reader is first familiarized with those features and principles of quantum mechanics providing a more efficient and secure information processing. Their applications to the general theory of information, cryptography, algorithms, computational complexity and error-correction are then discussed. Prospects for building a practical quantum computer are also analyzed.

2004

Interest toward information-theoretic derivations of the formalism of quantum theory has been growing since early 1990s thanks to the emergence of the field of quantum computation and to the return of epistemological questions into research programs of many theoretical physicists. We propose a system of information-theoretic axioms from which we derive the formalism of quantum theory.

IS4SI 2021, 2021

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Journal of Modern Physics, 2012

In this work some characteristics and applications for quantum information is revealed. The various dynamical equations of quantum information density have been investigated, transmission characteristics of the dynamical mutual information have been studied, and the decoherence-free controlling procedure has been considered, which exposes that quantum information is holographic through the similarity structure of subdynamic kinetic equations for quantum information density.

Entropy, 2016

The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material world has important consequences for the amounts of information that can be stored in physical systems and for the possibilities of information transfer. In many cases, overlap between quantum states (non-orthogonality of states) blurs distinctions and impedes efficient information transfer. However, the other typical quantum feature, entanglement, makes new and seemingly mysterious ways of transporting information possible. In this article, we suggest an interpretational scheme of quantum mechanics in terms of perspectival physical properties that may provide an intelligible account of these novel quantum possibilities, while staying close to the mathematical formalism of quantum mechanics.

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, di¤erences, and distinguishability, and is formalized using the distinctions ('dits') of a partition (a pair of points distinguished by the partition). All the de…nitions of simple, joint, conditional, and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding de…nitions at the logical level. The purpose of this paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates (cohered together in the pure su-perposition state being measured) that are distinguished by the measurement (decohered in the post-measurement mixed state). Both the classical and quantum versions of logical entropy have simple interpretations as " two-draw " probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states.