Groupoids and the tomographic picture of quantum mechanics

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.

References in corpus (7)

• Symplectic tomography as classical approach to quantum systems
• An introduction to the tomographic picture of quantum mechanics
• Alternative commutation relations, star products and tomography
• Density Matrix From Photon Number Tomography
• Star products, duality and double Lie algebras
• A tomographic setting for quasi-distribution functions
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Cited by in corpus (7)

• A gentle introduction to Schwinger's formulation of quantum mechanics: The groupoid picture
• Schwinger's Picture of Quantum Mechanics I: Groupoids
• Tomographic causal analysis of two-qubit states and tomographic discord
• Lie groupoids in information geometry
• The quantum-to-classical transition: contraction of associative products
• Generalized tomographic maps and star-product formalism
• The groupoid of bifractional transformations