On quantum vs. classical probability

Rau, Jochen

doi:10.1016/j.aop.2009.09.013

Cited by 23 publications

(33 citation statements)

References 79 publications

(100 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another set of axioms using tomographic locality was given by Marco Zaopo [45]. There has been much work recently by many people along less related lines (Fuchs [17], Goyal [19], Wilce [42], Rau [38,39], Fivel [13], . .…”

Section: A Personal History Of Reconstructionmentioning

confidence: 99%

Reconstructing Quantum Theory

Hardy

2015

Fundamental Theories of Physics

190

View full text Add to dashboard Cite

I provide operational postulates for quantum theory. These involve certain operational notions. Systems come in different types, a, b, c, . . .. A maximal set of distinguishable states is any set containing the maximum number, Na, of states for which there exists some measurement, called a maximal measurement, which can identify which state from the set we have in a single shot. A maximal effect is associated with each result of a maximal measurement. An informational face is the full set of states that give rise only to some subset of outcomes of some maximal measurements (it corresponds to constraining the system to have some reduced information carrying capacity). States are represented by vectors whose Ka entries are probabilities. A set of states is said to be non-flat if it is a spanning subset of some informational face. A filter is a transformation that passes unchanged those states in a given informational face while blocking those states in the complement informational face (that would give rise only to outcomes in the complement outcome set of the maximal measurement). Classical probability theory and quantum theory are the only two theories consistent with the following set of postulates.P1 Logical sharpness. There is a one-to-one map between pure states and maximal effects such that we get unit probability.P2 Information locality. A maximal measurement is effected on a composite system if we perform maximal measurements on each of the components (or, equivalently, N ab = NaN b ).P3 Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components (or, equivalently, K ab = KaK b ). P4′ Permutability. There exists a reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. P5 Sturdiness. Filters are non-flattening.To single out quantum theory we need only add any requirement that is inconsistent with classical probability theory and consistent with quantum theory.

show abstract

Section: A Personal History Of Reconstructionmentioning

confidence: 99%

Reconstructing Quantum Theory

Hardy

2015

Fundamental Theories of Physics

190

View full text Add to dashboard Cite

show abstract

“…One of the advantages ascribed to this approach was that the axioms imposed on a lattice structure could be given a clear operational interpretation: unlike the Hilbert space formulation, whose axioms have the disadvantage of being ad hoc and physically unmotivated, the quantum logical approach would be clearer and more intuitive from a physical point of view. But of course, the operational validity of the axioms imposed on the lattice structure was criticized by many authors (as an example, see [14]). …”

Section: The Quantum Logical Approach To Physicsmentioning

confidence: 99%

“…Quantum and classical probabilities have points in common as well as differences. These differences and the properties of quantum probabilities have been intensively studied in the literature [4,5,6,7,8,9,10,11,12,13,14]. It is important to remark that not all authors believe that quantum probabilities are essentially of a different nature than those which arise in probability theory (see for example [26] for a recent account).…”

Section: Introductionmentioning

confidence: 99%

“…One of the most important goals of OQL is to impose operationally motivated axioms on a lattice structure in order that it can be made isomorphic to a projection lattice on a Hilbert space. There are different positions in the literature about the question of whether this goal has been achieved or not [14], and also, of course, alternative operational approaches to physics, as the convex operational one [47,48,49,50,51,4]. In this work, we are interested in the great generality of the OQL approach.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A discussion on the origin of quantum probabilities

2014

View full text Add to dashboard Cite

We study the origin of quantum probabilities as arising from non-boolean propositionaloperational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorvian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case).

show abstract

“…Later, it was discovered that this was strongly related to the nonexistence of joint distributions for noncommuting observables. These peculiarities and formal aspects of the probabilities involved in quantum theory have been vastly studied in the literature [5][6][7][8][9][10][11]. One of the most important axiomatizations in probability theory is due to Kolmogorov [12].…”

Section: Introductionmentioning

confidence: 99%