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Title: 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, etc. 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 paper reviews the role of reference framesmore » and superselection rules in the theory of quantum-information processing.« less

Authors:
; ;  [1];  [2];  [2]
  1. School of Physics, The University of Sydney, Sydney, New South Wales 2006 (Australia)
  2. (United Kingdom)
Publication Date:
OSTI Identifier:
21013707
Resource Type:
Journal Article
Resource Relation:
Journal Name: Reviews of Modern Physics; Journal Volume: 79; Journal Issue: 2; Other Information: DOI: 10.1103/RevModPhys.79.555; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; COMMUNICATIONS; DEGREES OF FREEDOM; INFORMATION THEORY; QUANTUM COMPUTERS; QUANTUM CRYPTOGRAPHY; QUANTUM ENTANGLEMENT; QUANTUM INFORMATION; QUANTUM MECHANICS; SUPERSELECTION RULES

Citation Formats

Bartlett, Stephen D., Rudolph, Terry, Spekkens, Robert W., Optics Section, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom and Institute for Mathematical Sciences, Imperial College London, London SW7 2BW, and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA. Reference frames, superselection rules, and quantum information. United States: N. p., 2007. Web. doi:10.1103/REVMODPHYS.79.555.
Bartlett, Stephen D., Rudolph, Terry, Spekkens, Robert W., Optics Section, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom and Institute for Mathematical Sciences, Imperial College London, London SW7 2BW, & Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA. Reference frames, superselection rules, and quantum information. United States. doi:10.1103/REVMODPHYS.79.555.
Bartlett, Stephen D., Rudolph, Terry, Spekkens, Robert W., Optics Section, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom and Institute for Mathematical Sciences, Imperial College London, London SW7 2BW, and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA. Sun . "Reference frames, superselection rules, and quantum information". United States. doi:10.1103/REVMODPHYS.79.555.
@article{osti_21013707,
title = {Reference frames, superselection rules, and quantum information},
author = {Bartlett, Stephen D. and Rudolph, Terry and Spekkens, Robert W. and Optics Section, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom and Institute for Mathematical Sciences, Imperial College London, London SW7 2BW and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA},
abstractNote = {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, etc. 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 paper reviews the role of reference frames and superselection rules in the theory of quantum-information processing.},
doi = {10.1103/REVMODPHYS.79.555},
journal = {Reviews of Modern Physics},
number = 2,
volume = 79,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
  • In recent years it has become apparent that constraints on possible quantum operations, such as those constraints imposed by superselection rules (SSRs), have a profound effect on quantum information theoretic concepts like bipartite entanglement. This paper concentrates on a particular example: the constraint that applies when the parties (Alice and Bob) cannot distinguish among certain quantum objects they have. This arises naturally in the context of ensemble quantum information processing such as in liquid NMR. We discuss how a SSR for the symmetric group can be applied, and show how the extractable entanglement can be calculated analytically in certain cases,more » with a maximum bipartite entanglement in an ensemble of N Bell-state pairs scaling as log(N) as N{yields}{infinity}. We discuss the apparent disparity with the asymptotic (N{yields}{infinity}) recovery of unconstrained entanglement for other sorts of superselection rules, and show that the disparity disappears when the correct notion of applying the symmetric group SSR to multiple copies is used. Next we discuss reference frames in the context of this SSR, showing the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502 (2004)]. The action of a reference frame can be regarded as the analog of activation in mixed-state entanglement. We also discuss the analog of distillation: there exist states such that one copy can act as an imperfect reference frame for another copy. Finally we present an example of a stronger operational constraint, that operations must be noncollective as well as symmetric. Even under this stronger constraint we, nevertheless, show that Bell nonlocality (and hence entanglement) can be demonstrated for an ensemble of N Bell-state pairs no matter how large N is. This last work is a generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)].« less
  • We propose a quantum field theory of vortex solitons in the canonical formalism. Using the fact that the topological charge, regarded as an operator, commutes with all local operators, we obtain a superselection rule structure of Abelian and non-Abelian Higgs models in 2 + 1 dimensions. Lorentz-invariant vortex sectors are constructed as nonvacuum representations of the canonical commutation relations. The intertwinning operator between the vortex sector and the vacuum sector is identified to be a quantum vortex operator.
  • General structure properties of local and covariant gauge quantum field theories are investigated and a generalized cluster property is proved. Necessary and sufficient conditions are given for the failure of the cluster property which is strictly related to ''quark'' confinement. The deep relation between superselection rules and the infrared problems is discussed.
  • A theorem due to Wigner, which states that any transformation of a Hilbert space that preserves the absolute value of the inner products is equivalent to either a unitary or anti-unitary transformation, is considered. It is pointed out that two previous proofs of the theorem are not complete, and a new proof of the theorem, considered purely from the mathematical point of view, is given. The physical meanding of the theorem, and its connection with invariances and symmetries of physical systems, is then discussed. Particular attention is paid to the case in which superselection rales are present. A second proofmore » of the theorem is given. (auth)« less