The structure of classical extensions of quantum probability theory

Stulpe, Werner; Busch, Paul

doi:10.1063/1.2884581

Cited by 15 publications

(7 citation statements)

References 32 publications

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“…Moreover, it has been shown to be essentially unique by W. Stulpe and one of the authors [20]. This result provides formal support to the interpretation of indefinite quantum propositions in terms of degrees of reality defined by the quantum probabilities.…”

Section: Unsharp Quantum Reality and The Quantum-classical Contrastsupporting

confidence: 58%

Unsharp Quantum Reality

Busch

Jaeger

2010

Found Phys

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ABSTRACT. The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it a concept of joint properties. A property manifests itself as an element of unsharp reality by its power, or tendency, of becoming actual or actualizing a specific measurement outcome, where this tendency of actualization is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way.

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Section: Unsharp Quantum Reality and The Quantum-classical Contrastsupporting

confidence: 58%

Unsharp Quantum Reality

Busch

Jaeger

2010

Found Phys

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“…In [24] we also give simple explicit realizations of the classical statistical ensembles which describe the quantum system and its environment. In a formulation 1 In this context it may be interesting to compare our setting for probability distributions and observables to the so called "classical extension" of quantum statistical systems [18,20]. This mathematical approach shows certain similarities, but also important differences to our setting.…”

Section: Introductionmentioning

confidence: 93%

“…7 that the absence of knowledge of joint probabilities is a crucial aspect for the definition of correlations. The substate-probabilities (20) involve properties of the quantum system together with its environment. They are not accessible by measurements involving only the quantum system.…”

Section: Operations Among Probabilistic Observablesmentioning

confidence: 99%

Probabilistic observables, conditional correlations, and quantum physics

Wetterich

2010

Annalen der Physik

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We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated subsystem. The "coarse graining of the information" to micro-states implies probabilistic observables. For two-level probabilistic observables only a probability for finding the values one or minus one can be given for any micro-state, while such observables can be realized as classical observables with sharp values on a substate level. For a continuous family of micro-states parameterized by a sphere all the quantum mechanical laws for a two-state system follow under the assumption that the purity of the ensemble is conserved by the time evolution. The non-commutative correlation functions of quantum mechanics correspond to the use of conditional correlation functions in classical statistics. We further discuss the classical statistical realization of entanglement within a system corresponding to four-state quantum mechanics. We conclude that quantum mechanics can be derived from a classical statistical setting with infinitely many micro-states.Comment: substantially extended discussion of conditional correlations and probabilistic observables, new references 28 pages, 2 figure

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“…The correspondence E → f E =: R (E) defines a map R dual to R sending all quantum effects to classical effects [22]. Paul Busch and Werner Stulpe showed that the presentation of quantum mechanics via the maps R and R ensures that all quantum states and quantum effects have classical counterparts and is essentially unique [23], which enables the interpretation of indefinite quantum propositions via degrees of reality quantified by the quantum probabilities [1]: The probabilities tr[EP] can be viewed as measuring the fuzziness of the vague proposition represented by E, cf. [24].…”

Section: Phase Space For Unsharp Properties and Degree Of Realitymentioning

confidence: 99%

Quantum Unsharpness, Potentiality, and Reality

Jaeger

2019

Found Phys

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Paul Busch argued that the positive operator (valued) measure (POM), a generalization of the quantum observable, enables a consistent notion of unsharp reality based on a quantifiable degree of reality which systems can possess generalized properties jointly, whereas related sharp properties cannot be so possessed [1]. Here, the work leading up to the formalization of this notion to which he made great contributions is reviewed and explicated in relation to Heisenberg's notions of potentiality and actuality. The notion of unsharp reality is then extended further by the introduction of a distinction between actual and actualizable elements of reality based on these mathematical innovations.

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The structure of classical extensions of quantum probability theory

Cited by 15 publications

References 32 publications

Unsharp Quantum Reality

Unsharp Quantum Reality

Probabilistic observables, conditional correlations, and quantum physics

Quantum Unsharpness, Potentiality, and Reality

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