Weakly Jauch–Piron States in Effect Algebras

Abstract

We study various types of weakly Jauch–Piron states and various types of state-space properties in effect algebras. We generalize several results of Tkadlec (Tatra Mt. Math. Publ. 10, 55–62 1997; Algebra Universalis 61, 187–194 2009) and of Matoušek and Pták (Internat. J. Theoret. Phys. 54, 4476–4481 2015). In particular, we show when an effect algebra is an orthomodular poset, when a unital set of states is strongly order determining, and we present some state space characterizations of Boolean algebras.

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Acknowledgements

This work was supported by the project OPVVV CAAS CZ.02.1.01/0.0/0.0/ 16_019/0000778.

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Correspondence to Josef Tkadlec.

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Tkadlec, J. Weakly Jauch–Piron States in Effect Algebras. Int J Theor Phys (2021). https://doi.org/10.1007/s10773-020-04709-5

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Keywords

  • Effect algebra
  • Orthomodular poset
  • Boolean algebra
  • Maximality property
  • Weakly Jauch–Piron state
  • Unital set of states