Results 41 to 50 of about 1,569 (137)
Quantum information as a non-Kolmogorovian generalization of Shannon's theory [PDF]
, 2015 In this article we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting.
Bellomo, G., Bosyk, G. M., Holik, F.
core +4 more sources
Solvability of Generalized Orthomodular Lattices [PDF]
Pacific Journal of Mathematics, 1975 Suppose K is a given equational class of lattices (cf. I.26) and let ‵L be a lattice. Denote by E K (‵L) the set formed by those congruences T on ‵L for which ‵L/T∈K. Since ‵L/U∈K for the universal congruence U=L}L, E K (‵L) ≠ ∅. Define C K to be the intersection ∩{T; T∈E K (‵L)}. Then C K (‵L) is a congruence on ‵L. From I.25 we conclude that ‵L/C K (‵
openaire +4 more sources
Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements [PDF]
, 2010 We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras. Moreover, we prove that if such effect algebra $
Riecanova, Zdenka
core +6 more sources
Relatively orthomodular lattices
Discrete Mathematics, 2001 \textit{M.~F.~Janowitz} [``A note on generalized orthomodular lattices'', J. Nat. Sci. Math. 8, 89-94 (1968; Zbl 0169.02104)] defined a generalized orthomodular lattice (GOML) as a lattice with 0 and with an orthogonality relation (similar to that considered in orthomodular lattices (OMLs)).
openaire +2 more sources
Information-theoretic principle entails orthomodularity of a lattice
, 2005 Quantum logical axiomatic systems for quantum theory usually include a postulate that a lattice under consideration is orthomodular. We propose a derivation of orthomodularity from an information-theoretic axiom.
A. Grinbaum +34 more
core +3 more sources
The logic of causally closed spacetime subsets
, 2002 The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it.
Casini, H.
core +2 more sources
Scopes and Limits of Modality in Quantum Mechanics [PDF]
, 2006 We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular structure ...
Balbes +20 more
core +2 more sources
A presentation of Quantum Logic based on an "and then" connective
, 2007 When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information.
Lehmann, Daniel
core +1 more source
Quantum axiomatics and a theorem of M.P. Soler [PDF]
, 2000 Three of the traditional quantum axioms (orthocomplementation, orthomodularity and the covering law) show incompatibilities with two products introduced by Aerts for the description of joint entities.
Aerts, Diederik, Van Steirteghem, Bart
core +2 more sources
Commutators in Orthomodular Lattices
Demonstratio Mathematica, 1985 The author introduces the notions of a ''commutator'' for a possibly infinite set of elements M of an orthomodular lattice L and ''partial compatible'' (p.c.) for M with respect to some element \(a\in C(M)\) such that \(\{\) \(m\wedge a|\) \(m\in M\}\) is Boolean. If M is p.c. for \(a\in L\) then \(a\leq com(M)\) and CC(M) is p.c.
openaire +3 more sources