Higher-order interference and single-system postulates characterizing quantum theory

Barnum, Howard; Müller, Markus P.; Ududec, Cozmin

doi:10.1088/1367-2630/16/12/123029

Cited by 156 publications

(325 citation statements)

References 85 publications

(162 reference statements)

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“…However, taking into account the earlier successful predictions of the E principle [18][19][20][21][22][23] and the evidences of failure of other approaches [8][9][10], the result presented here promotes the E principle as the best option for understanding the limits of quantum contextual and nonlocal correlations. This apparent fundamental role of the E principle in QT is also supported by some recent results aiming to understand QT from fundamental physical principles [15,27,28].…”

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confidence: 62%

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Exclusivity principle and the quantum bound of the Bell inequality

Cabello

2014

Phys. Rev. A

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We show that, for general probabilistic theories admitting sharp measurements, the exclusivity principle together with two assumptions exactly singles out the Tsirelson bound of the Clauser-Horne-Shimony-Holt Bell inequality.Introduction.-Quantum theory (QT) is arguably the most accurate scientific theory of all times. Nevertheless, despite its mathematical simplicity, its fundamental principles are still unknown. In the quest for these principles, a key question is why QT is exactly as nonlocal [1] and contextual [2] as it is.There are two different approaches to answer this question. On one hand, the "black box" approach, which focuses on correlations among the outcomes of measurements in multipartite scenarios. This approach makes no assumptions on the internal working of the measurement devices (which are treated as black boxes) and pays no attention to the postmeasurement state of the system (since measurements are treated as if they were demolition measurements). Within this approach, it has been proven that the principles of information causality [3] and macroscopic locality [4], complemented by some assumptions, single out the maximum quantum violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [5,6] (i.e., the Tsirelson bound [7]). However, it has also been proven that these principles cannot exclude extremal nonlocal boxes prohibited in QT in the three-party, two-outcome, two-setting or (3, 2, 2) scenario [8,9]. Moreover, by its very definition, the black box approach cannot explain quantum contextual correlations [2]. In addition, there is increasing evidence that the black box approach, with independence of the principle invoked, cannot explain even quantum nonlocal correlations [10].On the other hand, the "sharp measurements," "graphtheoretic," or "contextuality" approach [11][12][13] focus on correlations among the outcomes of sharp measurements. For general probabilistic theories (GPTs), sharp measurements are nondemolition measurements that are repeatable and cause minimal disturbance [14,15]. In QT, sharp measurements are projective measurements [16]. In QT, generalized measurements are represented by positive operator-valued measures. However, in QT, any generalized measurement can always be implemented as a sharp measurement on the system and the environment [17].Within the sharp measurements approach, an "event" is defined as the postmeasurement state of the system after a sharp measurement. Two events are equivalent when they correspond to indistinguishable states. Two events are exclusive when there is a sharp measurement that perfectly distinguishes between them.The exclusivity (E) principle [18][19][20][21][22][23] states that any set of m pairwise exclusive events is m-wise exclusive. According to Kolmogorov's axioms of probability, the sum of the

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supporting

confidence: 62%

“…Later Specker conjectured that the E principle could be the fundamental principle of QT [26]. Recent works have shown that the E principle is implied by physical principles of a very different nature [15,27,28].…”

mentioning

confidence: 99%

Exclusivity principle and the quantum bound of the Bell inequality

Cabello

2014

Phys. Rev. A

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“…O is free to restrict his description of Q by erasing any questions from it that are redundant through equivalence. 9 As a result, every question vector q, if physically permitted at all, will correspond to a unique Q ∈ Q.…”

Section: How To Compute Probabilitiesmentioning

confidence: 99%

“…Among them are violation of the Bell [2,3] and more generally Clauser-Horne-Shimony-Holt inequalities [4], the 'no-signaling' principle [5] and, its generalization, 'information causality' [6], interference effects in mixtures [7], absence of third and higher order interference [8,9], a limit on the information content carried by systems [10][11][12][13][14][15][16][17][18][19][20][21][22] and others. However, all of these attributes yield incomplete characterizations, being shared by other probabilistic theories some of which admit unphysical correlation structures, as well as exotic information communication and processing tasks.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, there actually exist a number of successful reconstructions of finite dimensional quantum theory from operational axioms, most of which have been performed within the frameworks of generalized or operational probability theories [9,[23][24][25][26][27][28][29][30][31][32] (see also [33] which is adapted to a space-time language and the more mathematical reconstructions [34,35]). Despite the beauty and great technical achievements of some of these reconstructions, they arguably come short of providing a fully satisfactory physical and conceptual picture of quantum theory.…”

Section: Introductionmentioning

confidence: 99%

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Quantum theory from questions

2017

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We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S's state as O's 'catalogue of knowledge' about S. From the rules we derive the state spaces for N elementary systems and show that (a) they coincide with the set of density matrices over an N -qubit Hilbert space C 2 N ; (b) states evolve unitarily under the group PSU(2 N ) according to the von Neumann evolution equation; and (c) O's binary questions correspond to projective Pauli operator measurements with outcome probabilities given by the Born rule. As a by-product, this results in a propositional formulation of quantum theory. Aside from offering an informational explanation for the theory's architecture, the reconstruction also unravels new structural insights. We show that, in a derived quadratic information measure, (d) qubits satisfy inequalities which bound the information content in any set of mutually complementary questions to 1 bit; and (e) maximal sets of mutually complementary questions for one and two qubits must carry precisely 1 bit of information in pure states. The latter relations constitute conserved informational charges which define the unitary groups and, together with their conservation conditions, the sets of pure quantum states. These results highlight information as a 'charge of quantum theory' and the benefits of this informational approach. This work emphasizes the sufficiency of restricting to an observer's information to reconstruct the theory and completes the quantum reconstruction initiated in [1].

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Dynamical States and the Conventionality of (Non-) Classicality

Wilce

2020

Jerusalem Studies in Philosophy and History of Science

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Itamar Pitowsky long championed the view that quantum mechanics (QM) is best understood as a non-classical probability theory. Here, I want to offer some modest caveats. One is that QM is best seen, not as a new probability theory, but as something narrower, namely, a particular probabilistic theory-roughly, a class of probabilistic models, selected from within a much more general framework. It is this general framework that, if anything, deserves to be regarded as a "non-classical" probability theory. However, as I will also argue, this framework represents a very conservative extension of classical probability theory, essentially just eliding a tacit, and contingent, assumption in the latter that measurements or experiments can always be performed together. Moreover, for individual probabilistic models, and even for probabilistic theories, the distinction between "classical" and a "non-classical" is largely a conventional one, bound up with the question of what one means by the state of a system. In fact, for systems with a high degree of symmetry, including quantum mechanics, it is possible to interpret general probabilistic models as having a perfectly classical probabilistic structure, but an additional dynamical structure: states, rather than corresponding simply to probability measures, are represented as certain probability measure-valued functions on the system's symmetry group, and thus, as fundamentally dynamical objects. Conversely, a classical probability space equipped with reasonably well-behaved family of such "dynamical states" can be interpreted as a generalized probabilistic model in a canonical way. It is noteworthy that this "dynamical" representation is not a conventional hiddenvariables representation, and the question of what one means by "non-locality" in this setting is not entirely straightforward.

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Higher-order interference and single-system postulates characterizing quantum theory

Cited by 156 publications

References 85 publications

Exclusivity principle and the quantum bound of the Bell inequality

Exclusivity principle and the quantum bound of the Bell inequality

Quantum theory from questions

Dynamical States and the Conventionality of (Non-) Classicality

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