Operational Axioms for Quantum Mechanics

D’Ariano, Giacomo Mauro

doi:10.1063/1.2713449

Cited by 46 publications

(74 citation statements)

References 11 publications

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“…States, on this approach, are associated with preparation devices, and are regarded as compendia of probabil-ities regarding the outcomes of any measurement that can be performed. Similar discussions can be found in Holevo (1982), Ludwig (1983), andD'Ariano (2006).…”

Section: The Operational Approachsupporting

confidence: 72%

From physics to information theory and back

Myrvold¹

2010

Philosophy of Quantum Information and Entanglement

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Quantum information theory has given rise to a renewed interest in, and a new perspective on, the old issue of understanding the ways in which quantum mechanics differs from classical mechanics. The task of distinguishing between quantum and classical theory is facilitated by neutral frameworks that embrace both classical and quantum theory. In this paper, I discuss two approaches to this endeavour, the algebraic approach, and the convex set approach, with an eye to the strengths of each, and the relations between the two. I end with a discussion of one particular model, the toy theory devised by Rob Spekkens, which, with minor modifications, fits neatly within the convex sets framework, and which displays in an elegant manner some of the similarities and differences between classical and quantum theories. The conclusion suggested by this investigation is that Schrödinger was right to find the essential difference between classical and quantum theory in their handling of composite systems, though Schrödinger's contention that it is entanglement that is the distinctive feature of quantum mechanics needs to be modified.

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Section: The Operational Approachsupporting

confidence: 72%

From physics to information theory and back

Myrvold¹

2010

Philosophy of Quantum Information and Entanglement

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“…On the other hand, to urge that, similarly, the very ontology of a Many-Worlds interpretation presupposes a Hilbert space structure, would beg a very large question indeed. 15 Another possible objection is that a probabilistic/operational interpretation that takes "measurements" and "outcomes" as primitive cannot, in principle, accommodate cosmological questions, since one cannot make measurements on the entirety of space-time. But this is objection is hardly compelling.…”

Section: Summary and Further Questionsmentioning

confidence: 99%

“…There are, after all, many different ways to characterize classical probability theory, and the same is doubtless true of quantum probability theory. And, indeed, such answers as we have, for example, the axiomatic reconstructions of elementary quantum probability due to Hardy [27], Goyal [24], and D'Ariano [15] are based on very diverse considerations. Nor is the answer going to be such as to single out quantum models as uniquely reasonable: in the face of toy models like the Firefly Box, it seems extremely unlikely that the framework of Quantum Mechanics is in any sense a "law of thought".…”

Section: Characteristics Of Quantum Modelsmentioning

confidence: 99%

“…Fortunately, this isn't hard to achieve. Indeed, there is an essentially canonical formalism of generalized probability theory, developed more or less independently by many people, beginning perhaps with Mackey himself [33], and including Ludwig [32], Davies and Lewis [16], Edwards [18], Randall and Foulis [20], Holevo [28], and, more recently, Hardy [27], D'Ariano [15] and Barrett [6], among others. The next two subsections outline a version of this canonical formalism.…”

Section: General Probabilistic Modelsmentioning

confidence: 99%

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Formalism and Interpretation in Quantum Theory

Wilce

2010

Found Phys

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Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a "realistic" and "collapse-free" interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a simplified version of the Everett interpretation.

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“…In such applications the mathematical formalism of quantum mechanics is treated as an operational formalism, see, e.g., D' Ariano et al [20][21][22][23], for handling probabilistic data collected in aforementioned domains of research. This formalism works well for a wide class of effects, e.g., the disjunction effect and the order effect.…”

Section: Introductionmentioning

confidence: 99%

On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements

Basieva

Khrennikov

2015

Found Phys

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In this paper we study the problem of a possibility to use quantum observables to describe a possible combination of the order effect with sequential reproducibility for quantum measurements. By the order effect we mean a dependence of probability distributions (of measurement results) on the order of measurements. We consider two types of the sequential reproducibility: adjacent reproducibility ( A − A) (the standard perfect repeatability) and separated reproducibility(A − B − A). The first one is reproducibility with probability 1 of a result of measurement of some observable A measured twice, one A measurement after the other. The second one, A − B − A, is reproducibility with probability 1 of a result of A measurement when another quantum observable B is measured between two A's. Heuristically, it is clear that the second type of reproducibility is complementary to the order effect. We show that, surprisingly, this may not be the case. The order effect can coexist with a separated reproducibility as well as adjacent reproducibility for both observables A and B. However, the additional constraint in the form of separated reproducibility of the B − A − B type makes this coexistence impossible. The problem under consideration was motivated by attempts to apply the quantum formalism outside of physics, especially, in cognitive psychology and psychophysics. However, it is also important for foundations of quantum physics as a part of the problem about the structure of sequential quantum measurements.

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Operational Axioms for Quantum Mechanics

Cited by 46 publications

References 11 publications

From physics to information theory and back

From physics to information theory and back

Formalism and Interpretation in Quantum Theory

On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements

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