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pro vyhledávání: '"de Gosson, Maurice"'
Autor:
de Gosson, Maurice
Bopp shifts were introduced in 1956 in the study of statistical interpretations of quantum mechanics. They lead to a phase space view of quantum mechanics closely related to the Moyal star product and its interpretation as a deformation quantization.
Externí odkaz:
http://arxiv.org/abs/2411.14391
Autor:
de Gosson, Maurice
The aim of this paper is to suggest a new interpretation of quantum indeterminacy using the notion of polar duality from convex geometry. Our approach does not involve the usual variances and covariances, whose use to describe quantum uncertainties h
Externí odkaz:
http://arxiv.org/abs/2407.06684
Autor:
de Gosson, Maurice A.
Publikováno v:
Comptes Rendus. Mathématique, Vol 358, Iss 4, Pp 459-462 (2020)
We show that every Gaussian mixed quantum state can be disentangled by conjugation with a unitary operator corresponding to a symplectic rotation via the metaplectic representation of the symplectic group. The main tools we use are the Werner–Wolf
Externí odkaz:
https://doaj.org/article/8f7466440ebc4782a9cfabdba68bd53c
We derive Heisenberg uncertainty principles for pairs of Linear Canonical Transforms of a given function, by resorting to the fact that these transforms are just metaplectic operators associated with free symplectic matrices. The results obtained syn
Externí odkaz:
http://arxiv.org/abs/2405.10651
Autor:
de Gosson, Maurice A.
We address the problem of the reconstruction of quantum covariance matrices using the notion of Lagrangian and symplectic polar duality introduced in previous work. We apply our constructions to Gaussian quantum states which leads to a non-trivial ge
Externí odkaz:
http://arxiv.org/abs/2312.14823
Polar duality is a well-known concept from convex geometry and analysis. In the present paper, we study two symplectically covariant versions of polar duality keeping in mind their applications to quantum mechanics. The first variant makes use of the
Externí odkaz:
http://arxiv.org/abs/2309.07775
Autor:
de Gosson, Maurice
We show that the covariance matrix of a quantum state can be reconstructed from position measurements using the simple notion of polar duality, familiar from convex geometry. In particular, all multidimensional Gaussian states (pure or mixed) can in
Externí odkaz:
http://arxiv.org/abs/2301.12498
Autor:
de Gosson, Maurice
Werner and Wolf have proven in Phys. Rev. Lett. 86(16) (2001) a very elegant necessary and sufficient condition for a bosonic continuous variable bipartite Gaussian mixed quantum state to be separable. This condition is, however, difficult to impleme
Externí odkaz:
http://arxiv.org/abs/2210.01735
Autor:
de Gosson, Maurice
Toeplitz operators (also called localization operators) are a generalization of the well-known anti-Wick pseudodifferential operators studied by Berezin and Shubin. When a Toeplitz operator is positive semi-definite and has trace one we call it a den
Externí odkaz:
http://arxiv.org/abs/2209.08051
We use the notion of polar duality from convex geometry and the theory of Lagrangian planes from symplectic geometry to construct a fiber bundle over ellipsoids that can be viewed as a quantum-mechanical substitute for the classical symplectic phase
Externí odkaz:
http://arxiv.org/abs/2208.00470