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Introduction to Quantum Information Science$
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Vlatko Vedral

Print publication date: 2006

Print ISBN-13: 9780199215706

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199215706.001.0001

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Quantum information I

Quantum information I

Chapter:
(p.52) 5 Quantum information I
Source:
Introduction to Quantum Information Science
Author(s):

Vlatko Vedral

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199215706.003.0005

Information is often considered classical in a definite state rather than in a superposition of states. It seems rather strange to consider information in superpositions. Some people would, on the basis of this argument, conclude that quantum information can never exist and we can only have access to classical information. It turns out, however, that quantum information can be quantified in the same way as classical information using Shannon's prescription. There is a unique measure (up to a constant additive or multiplicative term) of quantum information such that S (the von Neumann entropy) is purely a function of the probabilities of outcomes of measurements made on a quantum system (that is, a function of a density operator); S is a continuous function of probability; S is additive. This chapter discusses the fidelity of pure quantum states, Helstrom's discrimination, quantum data compression, entropy of observation, conditional entropy and mutual information, relative entropy, and statistical interpretation of relative entropy.

Keywords:   quantum information, pure quantum states, Helstrom's discrimination, quantum data compression, entropy of observation, relative entropy, mutual information, von Neumann entropy

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