Non-signaling boxes and quantum logics
Tomasz Ignacy Tylec,Marek Kuś +1 more
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In this paper, a quantum logic approach is used to analyze the structure of non-signaling theories respecting relativistic causality, but allowing correlations violating bounds imposed by quantum mechanics such as CHSH inequality.Abstract:
Using a quantum logic approach we analyze the structure of the so-called non-signaling theories respecting relativistic causality, but allowing correlations violating bounds imposed by quantum mechanics such as CHSH inequality We discuss the relations among such theories, quantum mechanics, and classical physics Our main result is the construction of a probability theory adequate for the simplest instance of a non-signaling theory—the two non-signaling boxes world—in which we exhibit its differences in comparison with classical and quantum probabilities We show that the question of whether such a theory can be treated as a kind of 'generalization' of the quantum theory of the two-qubit system cannot be answered positively Some of its features put it closer to the quantum world—on the one hand, for example, the measurements are destructive, though on the other hand the Heisenberg uncertainty relations are not satisfied Another interesting property contrasting it from quantum mechanics is that the subset of 'classically correlated states', ie the states with only classical correlations, does not reproduce the classical world of the two two-state systems Our results establish a new link between quantum information theory and the well-developed theory of quantum logicsread more
Citations
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Randomness in quantum mechanics: philosophy, physics and technology
TL;DR: This progress report covers recent developments in the area of quantum randomness, which is an extraordinarily interdisciplinary area that belongs not only to physics, but also to philosophy, mathematics, computer science, and technology.
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Randomness in Quantum Mechanics: Philosophy, Physics and Technology
TL;DR: In this paper, the authors present a progress report on quantum randomness, which is an extraordinarily interdisciplinary area that belongs not only to physics, but also to philosophy, mathematics, computer science, and technology.
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Classical Logic and Quantum Logic with Multiple and Common Lattice Models
TL;DR: In this paper, it was shown that both classical logic and quantum logic have disjoint distributive and non-distributive ortholattices, and that they are sound and complete with respect to each of these lattices.
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Classical and Quantum Logics with Multiple and a Common Lattice Models
TL;DR: It is proved that both classical logic and quantum logic are sound and complete with respect to each of these lattices.
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Bell measurement ruling out supraquantum correlations
TL;DR: In this paper, a bipartite non-signaling box with three inputs per party was considered, and the set of measurements with just a single global measurement was extended to include quantum two-party Bell measurements.
References
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TL;DR: In this paper, a theorem of Bell, proving that certain predictions of quantum mechanics are inconsistent with the entire family of local hidden-variable theories, is generalized so as to apply to realizable experiments.
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Sandu Popescu,Daniel Rohrlich +1 more
TL;DR: In the conventional approach to quantum mechanics, indeterminism is an axiom and non-locality is a theorem as discussed by the authors, but in this paper, we consider inverting the logical order, making non-local non-quantum correlations, preserving relativistic causality, can violate the CHSH inequality more strongly than any quantum correlations.
Book ChapterDOI
The Logic of Quantum Mechanics
TL;DR: In this article, it was shown that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and that in particular one can never predict both the position and the momentum of S, (Heisenberg's Uncertainty Principle).
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The mathematical foundations of quantum mechanics
TL;DR: The Mathematical Foundations of Quantum Mechanics as mentioned in this paper were the first to provide a rigorous mathematical formulation of quantum theory and a systematic comparison with classical mechanics so that the full ramifications of the quantum revolution could be clearly revealed.
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On an Algebraic generalization of the quantum mechanical formalism
TL;DR: In this paper, it was shown that the statistical properties of the measurements of a quantum mechanical system assume their simplest form when expressed in terms of a certain hypercomplex algebra which is commutative but not associative.