Results 1  10
of
17
Contexts in quantum, classical and partition logic
 In Handbook of Quantum Logic
, 2006
"... Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud ..."
Abstract

Cited by 9 (8 self)
 Add to MetaCart
(Show Context)
Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud
Embedding Quantum Universes in Classical Ones
, 1999
"... this paper; the propositional structure encountered in the quantum mechanics of spin  state measurements of a spin onehalf particle along two directions ( mod p) , that is, the modular, orthocomplemented lattice MO 2 drawn in Fig. 1 ( where p 2 = ( p + ) and q 2 = ( q + ) ) ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
(Show Context)
this paper; the propositional structure encountered in the quantum mechanics of spin  state measurements of a spin onehalf particle along two directions ( mod p) , that is, the modular, orthocomplemented lattice MO 2 drawn in Fig. 1 ( where p 2 = ( p + ) and q 2 = ( q + ) )
Experimental nonclassicality of an indivisible quantum system, Nature 274
, 2011
"... Experimental nonclassicality of an indivisible quantum system ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Experimental nonclassicality of an indivisible quantum system
Quantum logic. A brief outline
, 2005
"... A more complete introduction of the author can be found in the book ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
A more complete introduction of the author can be found in the book
Generalizations of Kochen and Specker’s theorem and the effectiveness of Gleason’s theorem
 Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35, 177194
, 2004
"... Abstract. Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s th ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Abstract. Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated. 1. Gleason’s Theorem and Logical Compactness Kochen and Specker’s (1967) theorem (KS) puts a severe constraint on possible hiddenvariable interpretations of quantum mechanics. Often it is considered an improvement on a similar argument derived from Gleason (1957) theorem (see, for example, Held. 2000). This is true in the sense that KS provide an explicit construction of a finite set of rays on which no twovalued homomorphism exists. However, the fact that there is such a finite set follows from Gleason’s theorem using a simple logical compactness argument (Pitowsky 1998, a similar point is made in Bell 1996). The existence of finite sets of rays with other interesting features
Twelvedimensional Pauli group contextuality
 2012
"... Abstract. The goal of the paper is to check whether the real eigenstates of the observables in the single qudit Pauli group may lead to quantum contextuality, the property that mutually compatible and independent experiments depend on each other. We find ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract. The goal of the paper is to check whether the real eigenstates of the observables in the single qudit Pauli group may lead to quantum contextuality, the property that mutually compatible and independent experiments depend on each other. We find
An obstruction based approach to the KochenSpecker theorem
, 1999
"... In [1] it was shown that the Kochen Specker theorem can be written in terms of the nonexistence of global elements of a certain varying set over the category W of boolean subalgebras of projection operators on some Hilbert space H. In this paper, we show how obstructions to the construction of such ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
In [1] it was shown that the Kochen Specker theorem can be written in terms of the nonexistence of global elements of a certain varying set over the category W of boolean subalgebras of projection operators on some Hilbert space H. In this paper, we show how obstructions to the construction of such global elements arise, and how this provides a new way of looking at proofs of the theorem.
A Flea on Schrödinger’s Cat
, 2013
"... We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the postmeasurement ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the postmeasurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this theory, or introduce unusual and controversial interpretative rules and/or ontologies). To that effect, we recall a remarkable phenomenon in the theory of Schrödinger operators (discovered in 1981 by JonaLasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric doublewell Hamiltonian (which is paradigmatically of Schrödinger’s Cat type) becomes exponentially sensitive to tiny perturbations of the potential as ~ → 0. We show that this instability emerges also from the textbook wkb approximation, extend it to timedependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which
Quantum logic. A brief outline
, 2005
"... Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical evidence of the quantum world. We give a brief outline of quant ..."
Abstract
 Add to MetaCart
Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical evidence of the quantum world. We give a brief outline of quantum logic, and some of its algebraic properties, such as nondistributivity, whereby emphasis is given to concrete experimental setups related to quantum logical entities. A probability theory based on quantum logic is fundamentally and sometimes even spectacularly different from probabilities based on classical Boolean logic. We give a brief outline of its nonclassical aspects; in particular violations of BooleBell type consistency constraints on joint probabilities, as well as the KochenSpecker theorem, demonstrating in a constructive, finite way the scarcity and even nonexistence of twovalued states interpretable as classical truth assignments. A more complete introduction of the author can be found in the book Quantum Logic (Springer, 1998)