Keywords: finite atomistic quantum logic; orthomodular lattice; conditional state; s-map; d-map; bivariable functions; modeling infimum measure; supremum measure; simultaneous measurements
@article{KYB_2010_46_6_a5,
author = {Drobn\'a, Eva and N\'an\'asiov\'a, O\'lga and Val\'a\v{s}kov\'a, \'Lubica},
title = {Quantum logics and bivariable functions},
journal = {Kybernetika},
pages = {982--995},
year = {2010},
volume = {46},
number = {6},
mrnumber = {2797422},
zbl = {1229.03054},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KYB_2010_46_6_a5/}
}
Drobná, Eva; Nánásiová, Oĺga; Valášková, Ĺubica. Quantum logics and bivariable functions. Kybernetika, Tome 46 (2010) no. 6, pp. 982-995. http://geodesic.mathdoc.fr/item/KYB_2010_46_6_a5/
[1] Al-Adilee, A. M., Nánásiová, O.: Copula and s-map on a quantum logic. Inform. Sci. 179 (2009), 4199–4207. | DOI | MR | Zbl
[2] Dohnal, G.: Markov property in quantum logic. A reflection. Inform. Sci. 179 (2009), 485–491. | DOI | MR | Zbl
[3] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structure. Kluwer Acad. Publishers, Dortrecht/Boston/London, Ister Science, Bratislava 2000. | MR
[4] Greechie, R. J.: Orthogonal lattices admitting no states. J. Combin. Theory, Ser. A10 (1971), 119–132. | DOI | MR
[5] Kalmbach, G.: Orthomodular Lattices. Academic Press, London 1983. | MR | Zbl
[6] Nánásiová, O.: Map for simultaneous measurements for a quantum logic. Internat. J. Theoret. Phys. 42 (2003), 1889–1903. | DOI | MR | Zbl
[7] Nánásiová, O.: Principle conditioning. Internat. J. Theoret. Phys. 43 (2004), 1757–1767. | DOI | MR | Zbl
[8] Nánásiová, O., Khrennikov, A.: Representation theorem for observables on a quantum system. Internat. J. Theoret. Phys. 45 (2006), 469–482. | DOI | MR
[9] Nánásiová, O., Khrennikov, A.: Compatibility and marginality. Internat. J. Theoret. Phys. 46 (2007) 1083–1095. | DOI | MR | Zbl
[10] Nánásiová, O., Pulmannová, S.: S-map and tracial states. Inform. Sci. 179 (2009) 515–520. | DOI | MR | Zbl
[11] Nánásiová, O., Trokanová, K., Žembery, I.: Commutative and non commutative s-maps. Forum Statist. Slovacum 2 (2007) 172–177.
[12] Nánásiová, O., Valášková, L’.: Maps on a quantum logic. Soft Computing (2009). doi:10.1007/s00500-009-0483-4
[13] Nánásiová, O., Valášková, L’.: Marginality and triangle inequality Internat. J. Theoret. Phys. (2010), accepted. | MR
[14] Navara, M.: An othomodular lattice admitting no group-valued measure. Proc. Amer. Math. Soc. 122 (1994), 7–12. | DOI | MR
[15] Neumann, J. von: Mathematische Grundlagen der Quantenmechanik. Springer-Verlag, Berlin 1932. | MR
[16] Pták, P., Pulmannová, S.: Quantum Logics. Kluwer Acad. Press, Bratislava 1991. | MR
[17] Varadarajan, V.: Geometry of Quantum Theory. D. Van Nostrand, Princeton, New Jersey 1968. | MR | Zbl