Probability Measures and Projections on Quantum Logics

被引：0

作者：

Nanasiova, Olga ^{[1
]}

Cernanova, Viera ^{[2
]}

Valaskova, Lubica ^{[3
]}

机构：

[1] Slovak Univ Technol Bratislava, Inst Comp Sci & Math, Ilkovicova 3, Bratislava 81219, Slovakia

[2] Trnava Univ, Fac Educ, Dept Math & Comp Sci, Priemyselna 4, Trnava 91843, Slovakia

[3] Slovak Univ Technol Bratislava, Dept Math & Descript Geometry, Radlinskeho 11, Bratislava 81005, Slovakia

来源：

INFORMATION TECHNOLOGY, SYSTEMS RESEARCH, AND COMPUTATIONAL PHYSICS | 2020年 / 945卷

关键词：

Logical connectives; Orthomodular lattice; Quantum logic; Probability measure; State; CONJUNCTION;

D O I：

10.1007/978-3-030-18058-4_25

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The present paper is devoted to modelling of a probability measure of logical connectives on a quantum logic (QL), via a G-map, which is a special map on it. We follow the work in which the probability of logical conjunction, disjunction and symmetric difference and their negations for non-compatible propositions are studied. We study such a G-map on quantum logics, which is a probability measure of a projection and show, that unlike classical (Boolean) logic, probability measure of projections on a quantum logic are not necessarilly pure projections. We compare properties of a G-map on QLs with properties of a probability measure related to logical connectives on a Boolean algebra.

引用

页码：321 / 330

页数：10

共 26 条

[1] The logic of quantum mechanics
Birkhoff, G
von Neumann, J
[J]. ANNALS OF MATHEMATICS, 1936, 37 : 823 - 843
[2] QUANTUM-LOGICS WITH JAUCH-PIRON STATES
BUNCE, LJ
NAVARA, M
PTAK, P
WRIGHT, JDM
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1985, 36 (143) : 261 - 271
[3] Drobná E, 2010, KYBERNETIKA, V46, P982
[4] Dvurecenskij A., 2000, NEW TRENDS QUANTUM S
[5] Dvurecenskij A, 1984, REPORTS MATH PHYSICS, V19, P349
[6] Herman L., 1975, Notre Dame Journal of Formal Logic, V16, P305, DOI 10.1305/ndjfl/1093891789
[7] JAUCH JM, 1969, HELV PHYS ACTA, V42, P842
[8] Khrennikov A, 2009, FDN PROBABILITY PHYS
[9] [Хренников Андрей Юрьевич Khrennikov Andrei Yur'evich], 2008, [Теоретическая и математическая физика, Theoretical and Mathematical Physics, Teoreticheskaya i matematicheskaya fizika], V157, P99, DOI 10.4213/tmf6266
[10] Principle conditioning
Nánásiová, O
[J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2004, 43 (7-8) : 1757 - 1767

← 1 2 3 →