Particle-wave duality: a dichotomy between symmetry and asymmetry

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Title Particle-wave duality: a dichotomy between symmetry and asymmetry
Author Vaccaro, Joan
Journal Name Proceedings of the Royal Society A
Year Published 2012
Place of publication United Kingdom
Publisher The Royal Society Publishing
Abstract Symmetry plays a central role in many areas of modern physics. Here, we show that it also underpins the dual particle and wave nature of quantum systems.We begin by noting that a classical point particle breaks translational symmetry, whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by log(D), where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus a more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators.
Peer Reviewed Yes
Published Yes
Alternative URI http://dx.doi.org/10.1098/rspa.2011.0271
Copyright Statement Copyright 2012 Royal Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal website for access to the definitive, published version.
Volume 468
Issue Number 2140
Page from 1065
Page to 1084
ISSN 1471-2946
Date Accessioned 2012-03-20; 2012-09-10T23:20:48Z
Date Available 2012-09-10T23:20:48Z
Faculty Faculty of Science, Environment, Engineering and Technology
Subject Quantum Physics
URI http://hdl.handle.net/10072/46753
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1

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