International Journal of Theoretical Physics

, Volume 50, Issue 12, pp 3635–3645 | Cite as

Quantum Axiomatics: Topological and Classical Properties of State Property Systems

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Abstract

The definition of ‘classical state’ from (Aerts in K. Engesser, D. Gabbay and D. Lehmann (Eds.), Handbook of Quantum Logic and Quantum Structures. Elsevier, Amsterdam, 2009), used e.g. in Aerts et al. (http://arxiv.org/abs/quant-ph/0503083, 2010) to prove a decomposition theorem internally in the language of State Property Systems, presupposes as an additional datum an orthocomplementation on the property lattice of a physical system. In this paper we argue on the basis of the (ε,d)-model on the Poincaré sphere that a notion of topologicity for states can be seen as an alternative (operationally foundable) classicality notion in the absence of an orthocomplementation, and compare it to the known and operationally founded concept of classicality.

Keywords

State property system Orthocomplementation Property lattice Closure space Classical property 

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Centre Leo Apostel and Department of MathematicsVrije Universiteit BrusselBrusselsNetherlands
  2. 2.Department of MathematicsVrije Universiteit BrusselBrusselsNetherlands

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