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Local Representations of Rotations on Discrete Configuration Spaces

  • Michael J. W. HallEmail author
  • Marcel Reginatto
Chapter
  • 693 Downloads
Part of the Fundamental Theories of Physics book series (FTPH, volume 184)

Abstract

A spin-half system may be characterised as having a set of two-valued observables which generate infinitesimal rotations in three dimensions. This abstract formulation can be given a concrete realization using ensembles on configuration space. We derive very general probabilistic models for ensembles that consist of one and two spin-half systems. In the case of a single spin-half system, there are two main requirements that need to be satisfied: the configuration space must be a discrete set, labelling the outcomes of two-valued spin observables, and these observables must provide a representation of so(3). These two requirements are sufficient to lead to a model which is equivalent to the quantum theory of a single qubit. The case of a pair of spin-half systems is more complicated, in that additional physical requirements concerning locality and subsystem independence must also be taken into account, and now the observables must provide a representation of \(so(3) \oplus so(3)\). We show in this case that, in addition to a model equivalent to the quantum theory of a pair of qubits, it may also be possible to have non-quantum local models.

Keywords

Poisson Bracket Configuration Space Canonical Transformation Bell Inequality Spin Measurement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Centre for Quantum DynamicsGriffith UniversityBrisbaneAustralia
  2. 2.Physikalisch-Technische BundesanstaltBraunschweigGermany

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