How quantum is a quantum ensemble?

How quantum is a quantum ensemble? In the Hilbert space operator formalism of quantum mechanics, a single quantum state, which is represented by a density operator, can be regarded as classical in the sense that it can always be diagonalized. However, a quantum ensemble, which is represented by a family of quantum states together with a probability distribution specifying the probability of the occurrence of each state, cannot be diagonalized simultaneously in generic cases, and possesses intrinsic quantum features as long as the involved quantum states are not commutative. The natural question arises as how to quantify its quantumness. By virtue of a canonical correspondence between quantum ensembles and classical-quantum bipartite states, we propose an intuitive entropic quantity which captures certain quantum features of quantum ensembles, and compare it with that defined as the gap between the Holevo quantity and the accessible information. Implications for quantum cryptography and relations to quantum channel capacities are indicated. Some illustrative examples are worked out. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

How quantum is a quantum ensemble?

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Publisher
Springer US
Copyright
Copyright © 2010 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-010-0162-5
Publisher site
See Article on Publisher Site

Abstract

In the Hilbert space operator formalism of quantum mechanics, a single quantum state, which is represented by a density operator, can be regarded as classical in the sense that it can always be diagonalized. However, a quantum ensemble, which is represented by a family of quantum states together with a probability distribution specifying the probability of the occurrence of each state, cannot be diagonalized simultaneously in generic cases, and possesses intrinsic quantum features as long as the involved quantum states are not commutative. The natural question arises as how to quantify its quantumness. By virtue of a canonical correspondence between quantum ensembles and classical-quantum bipartite states, we propose an intuitive entropic quantity which captures certain quantum features of quantum ensembles, and compare it with that defined as the gap between the Holevo quantity and the accessible information. Implications for quantum cryptography and relations to quantum channel capacities are indicated. Some illustrative examples are worked out.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 11, 2010

References

  • Quantifying entanglement
    Vedral, V.; Plenio, M.B.; Rippin, M.A.; Knight, P.L.

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