Groupoids and the tomographic picture of quantum mechanics
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TLDR
The relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces is discussed in this paper, where the realizations of groupoid algebras based on qudit, photon-number (Fock) states and symplectic tomography quantizers and dequantizers are constructed.Abstract:
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit, photon-number (Fock) states and symplectic tomography quantizers and dequantizers will be constructed. Conditions for identifying the convolution product of groupoid functions and the star product arising from a quantization–dequantization scheme will be given. A tomographic approach to construct quasi-distributions out of suitable immersions of groupoids into Hilbert spaces will be formulated and, finally, intertwining kernels for such generalized symplectic tomograms will be evaluated explicitly.read more
Citations
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Schwinger’s picture of quantum mechanics I: Groupoids
TL;DR: A new picture of Quantum Mechanics based on the theory of groupoids is presented in this article, which provides the mathematical background for Schwinger's algebra of selective measurements and helps to un...
Journal ArticleDOI
A gentle introduction to Schwinger’s formulation of quantum mechanics: The groupoid picture
TL;DR: In this article, the mathematical structure behind Schwinger's symbolism of atomic measurements is shown to be a groupoid, and it is shown that the symbolism can be represented by a group of groups.
Journal ArticleDOI
Schwinger's Picture of Quantum Mechanics I: Groupoids
TL;DR: A new picture of quantum mechanics based on the theory of groupoids is presented in this paper, which provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual applications.
Journal ArticleDOI
Tomographic causal analysis of two-qubit states and tomographic discord
TL;DR: In this paper, a novel approach to definition of asymmetry in quantum bipartite state based on its tomographic Shannon entropies is proposed, where two measurement bases are considered: one that diagonalizes density matrices of subsystems and is used in a definition of tomographic discord, and the second one that maximizes Shannon mutual information and relates to symmetrical form quantum discord.
Journal ArticleDOI
The quantum-to-classical transition: contraction of associative products
Alberto Ibort,Alberto Ibort,Vladimir I. Man’ko,Vladimir I. Man’ko,Giuseppe Marmo,Andrea Simoni,Cosimo Stornaiolo,Franco Ventriglia +7 more
TL;DR: In this article, the quantum-to-classical transition from the point of view of contractions of associative algebras is considered from the perspective of the quantum case.
References
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TL;DR: In this article, an attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics, which may hence be considered as an interpretation of quantum kinematics.
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Ordered Expansions in Boson Amplitude Operators
Kevin Cahill,Roy J. Glauber +1 more
TL;DR: In this article, a parametric ordering convention is introduced according to which normal, symmetric, and antinormal ordering correspond to the values $s=+1,0,\ensuremath{-}1, respectively, of an order parameter $s$.
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On the Principles of Elementary Quantum Mechanics
TL;DR: In this paper, the statistical character of quantum mechanics is analyzed by averaging over uniquely determined processes as in classical statistical mechanics (interpretation) with respect to the notion of observability.