The Symmetry Group of Gaussian States in $${L}^{2}({\mathbb{R}}^{n})$$

DOI10.1007/978-3-642-33549-5_21zbMath1275.81059arXiv1101.5041OpenAlexW1636561508MaRDI QIDQ2838154

K. R. Parthasarathy

Publication date: 8 July 2013

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.5041

zbMATH Keywords

symplectic groupWeyl operatorsGaussian statemomentum and position observablesBogolioubov automorphism

Mathematics Subject Classification ID

Noncommutative probability and statistics (46L53) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Quantum stochastic calculus (81S25) Geometry and quantization, symplectic methods (81S10) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (15)

Exchangeable, stationary, and entangled chains of Gaussian states ⋮ Symplectic dilations, Gaussian states and Gaussian channels ⋮ Quantum stochastic calculus and quantum Gaussian processes ⋮ On symplectic eigenvalues of positive definite matrices ⋮ Log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter ⋮ Computation of sandwiched relative α-entropy of two n-mode Gaussian states ⋮ On the equivalence of separability and extendability of quantum states ⋮ On a Characterization of Gaussian Transition Operators ⋮ Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem ⋮ Infinite mode quantum Gaussian states ⋮ Some inequalities for eigenvalues and symplectic eigenvalues of positive definite matrices ⋮ On generalizing trace minimization principles ⋮ A common parametrization for finite mode Gaussian states, their symmetries, and associated contractions with some applications ⋮ A pedagogical note on the computation of relative entropy of two \(n\)-mode Gaussian states ⋮ Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization

Cites Work

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