Skip to main content
SpringerLink
Log in

Maps on a quantum logic

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this paper we will study functions G of two variables on a quantum logic L, such that for each compatible elements \(a,b\in L,\) \(G(a,b)=m(a\wedge b)\) or \( G(a,b)=m(a\vee b)\) or \(G(a,b)=m(a\triangle b),\) where m is a state on L.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Beltrametti E, Bugajski S (2004) Separating classical and quantum correlations. Int J Theor Phys 43(7–8):1793–1801

    Article  MATH  MathSciNet  Google Scholar 

  • Bohdalová M, Minárová M, Nánásiová O (2006) A note to algebraic approach to uncertainty. Forum Stat Slov 3:31–39

    Google Scholar 

  • Chovanec F, Kôpka F (2007) D-posets. In: Engesser K, Gabbay DM, Lehmanm D (eds) Handbook of quantum logic and quantum structures: quantum structures. Elsevier, Amsterdam, pp 367–428

  • Chovanec F, Rybáriková E (1998) Ideal and filters in D-poset. Int J Thoer Phys 37:17–22

    Article  MATH  Google Scholar 

  • Dohnal G (2009) Markov property in quantum logic. A reflection Inf Sci 179:485–491

    Google Scholar 

  • Dvurečenskij A, Pulmannová S (2000) New trends in quantum structures. Kluwer Academic Publishers, Bratislava

  • Greechie RJ (1971) Orthogonal lattices admitting no states. J Combin Theory Ser A 10:119–132

    Article  MATH  MathSciNet  Google Scholar 

  • Kalina M, Nánásiová O (2006) Conditional states and joint distributions on MV-algebras. Kybernetika 42:129–142

    MathSciNet  Google Scholar 

  • Kolmogorov AN (1950) Foundation of the theory of probability. Chelsea Press, New York (German original appeared in 1933)

    Google Scholar 

  • Nánásiová O (2003) Map for simultaneous measurements for a quantum logic. Int J Theor Phys 42:1889–1903

    Article  MATH  Google Scholar 

  • Nánásiová O, Minárová M, Mohammed A (2006) Measure of “symmetric difference”. Proc Magia 2006:55–60

    Google Scholar 

  • Nánásiová O, Pulmannová S (2009) S-map and tracial states. Inf Sci 179:515–520

    Google Scholar 

  • Navara M (1994) An othomodular lattice admitting no group-valued measure. Proc Am Math Soc 122(1):7–12

    Article  MATH  MathSciNet  Google Scholar 

  • Pták P, Pulmannová S (1991) Quantum logics, Kluwer Academic Press, Bratislava

    MATH  Google Scholar 

  • Riečanová Z (2000)Generalization of blocks for D-lattices and lattice-ordered effect algebras. Int J Theor Phys 39(2):231–237

    Article  MATH  Google Scholar 

  • Varadarajan V (1968) Geometry of quantum theory. D. Van Nostrand, Princeton

Download references

Acknowledgments

This work was supported by Science and Technology Assistance Agency under the contract No. APVV-0375-06, VEGA-1/0373/08, VEGA 1/4024/07.

Author information

Authors and Affiliations

  1. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Radlinského 11, 813 68, Bratislava, Slovak Republic

    Oľga Nánásiová & Ľubica Valášková

Authors
  1. Oľga Nánásiová
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ľubica Valášková
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oľga Nánásiová.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nánásiová, O., Valášková, Ľ. Maps on a quantum logic. Soft Comput 14, 1047–1052 (2010). https://doi.org/10.1007/s00500-009-0483-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-009-0483-4

Keywords

Search

Navigation