Asymmetry properties of pure quantum states

Iman Marvian and Robert W. Spekkens
Phys. Rev. A 90, 014102 – Published 30 July 2014

Abstract

The asymmetry properties of a state relative to some symmetry group specify how and to what extent the given symmetry is broken by the state. Characterizing these is found to be surprisingly useful for addressing a very common problem: to determine what follows from a system's dynamics (possibly open) having that symmetry. We demonstrate and exploit the fact that the asymmetry properties of a state can be understood in terms of information-theoretic concepts. We show that for a pure state ψ and a symmetry group G, they are completely specified by the characteristic function of the state, defined as χψ(g)ψ|U(g)|ψ, where gG and U is the unitary representation of interest. Based on this observation, we study several important problems about the interconversion of pure states under symmetric dynamics, such as determining the conditions for reversible transformations, deterministic irreversible transformations, and asymptotic transformations.

  • Received 11 May 2011

DOI:https://doi.org/10.1103/PhysRevA.90.014102

©2014 American Physical Society

Authors & Affiliations

Iman Marvian1,2,3 and Robert W. Spekkens1

  • 1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
  • 2Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 3Department of Physics and Astronomy, Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA

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Issue

Vol. 90, Iss. 1 — July 2014

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