The theory of manipulations of pure state asymmetry: I. Basic tools, equivalence classes and single copy transformations
By Iman Marvian, Robert W. Spekkens. 2011
217 citations recorded by the source corpus.
If a system undergoes symmetric dynamics, then the final state of the system 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 ψ relative to the symmetry group G are completely specified by the characteristic function of the state, defined as χψ(g) ≡ 〈ψ|U(g)|ψ〉 where g∈G and U is the unitary representation of interest. For a symmetry described by a compact Lie group G, we show that two pure states can be reversibly interconverted one to the other by symmetric operations if and only if their characteristic functions are equal up to a one-dimensional representation of the group. Characteristic functions also allow us to easily identify the conditions for one pure state to be converted to another by symmetric operations (in general irreversibly) for the various paradigms of single-copy transformations: deterministic, state-to-ensemble, stochastic and catalyzed.
Subfields: Astronomy and Astrophysics, Materials Chemistry, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/6d23b3cb8650ea2033880972f6ccde11839e20c8
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Citations in the corpus
- Quantum resource theories (2018, background): “Recently, it was shown by Marvian and Spekkens (2013, 2014a) that the QRT of asymmetry provides a systematic way to capture all the consequences of symmetric evolution.”
- Description of quantum coherence in thermodynamic processes requires constraints beyond free energy (2014, background): “Exploiting recent results in asymmetry theory [22, 23], we show that thermodynamics can be viewed as being determined by at least two independent resources: the first is quantified by known free energies and measures how far a state is from being thermal; the second, a missing ingredient of previous”