Reference frames, superselection rules, and quantum information

Abstract

Recently, there has been much interest in a new kind of ``unspeakable'' quantum information that stands to regular quantum information in the same way that a direction in space or a moment in time stands to a classical bit string: the former can only be encoded using particular degrees of freedom while the latter are indifferent to the physical nature of the information carriers. The problem of correlating distant reference frames, of which aligning Cartesian axes and synchronizing clocks are important instances, is an example of a task that requires the exchange of unspeakable information and for which it is interesting to determine the fundamental quantum limit of efficiency. There have also been many investigations into the information theory that is appropriate for parties that lack reference frames or that lack correlation between their reference frames, restrictions that result in global and local superselection rules. In the presence of these, quantum unspeakable information becomes a new kind of resource that can be manipulated, depleted, quantified, etcetera. Methods have also been developed to contend with these restrictions using relational encodings, particularly in the context of computation, cryptography, communication, and the manipulation of entanglement. This article reviews the role of reference frames and superselection rules in the theory of quantum information processing.

55 pages, published version

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Cited by in corpus (15)

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• Robust photonic entanglement distribution via state-independent encoding onto decoherence-free subspace
• Parameter Estimation with Mixed-State Quantum Computation
• Quantum reference frames and deformed symmetries
• The Computational Power of Symmetric Hamiltonians
• Quantum Reference Frames and the Classification of Rotationally-Invariant Maps
• Non-locality of non-Abelian anyons
• Unambiguous identification of coherent states II: Multiple resources
• Fundamental destruction of information and conservation laws
• Symmetric construction of reference-frame-free qudits
• Quantum mechanical observer and superstring/M theory
• Time-reversal frameness and superselection
• Quantum mechanical observers: a phase space approach
• Quantum tetrahedron and its classical limit