The theory of manipulations of pure state asymmetry I: basic tools and equivalence classes of states under symmetric operations

Details The theory of manipulations of pure state asymmetry I: basic tools and equivalence classes of states under symmetric operations The theory of manipulations of pure state asymmetry I: basic tools and equivalence classes of states under symmetric operations

2011-03-31

arxiv.org/abs/1104.0018v1

Physics

Quantum Physics

22 Pages, 2 Figures, Comments welcome

Scientific paper

If the initial state of a system and its dynamical equations are both symmetric, which is to say invariant under a symmetry group of transformations, then the final state will also be symmetric. This implies that under symmetric dynamics any symmetry-breaking in the final state must have its origin in the initial state. Specifically, the final state can only break the symmetry in ways in which it was broken by the initial state, and its measure of asymmetry can be no greater than that of the initial state. It follows that for the purpose of understanding the consequences of symmetries of dynamics, in particular, complicated and open-system dynamics, it is useful to introduce the notion of a state's asymmetry properties, which includes the type and measure of its asymmetry. We demonstrate and exploit the fact that the asymmetry properties of a state can also be understood in terms of information-theoretic concepts, for instance in terms of the state's ability to encode information about an element of the symmetry group. We show that the asymmetry properties of a pure state psi relative to the symmetry group G are completely specified by the characteristic function of the state, defined as chi_psi(g)= where g\in G and U is the unitary representation of interest. Among other results, we show that for a symmetry described by a compact Lie group G, two pure states can be reversibly interconverted one to the other by symmetric dynamics if and only if their characteristic functions are equal up to a 1-dimensional representation of the group.

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