Related papers: The decoherence-free subalgebra of Gaussian Quantum Markov Semigroups

The decoherence-free subalgebra of Gaussian Quantum Markov Semigroups

URL: http://arxiv.org/abs/2112.13781v2
Date: Sat, 27 Aug 2022 13:56:38 GMT
Title: The decoherence-free subalgebra of Gaussian Quantum Markov Semigroups
Authors: Juli\'an Agredo, Franco Fagnola, Damiano Poletti
Abstract summary: We show that $mathcalN(mathcalT)$ is a type I von Neumann algebra $Linfty(mathbbRd_c;mathbbC)barotimesmathcalB(Gamma(Gamma(mathbbCd))$ determined, up to unitary equivalence, by two natural numbers $d_c,d_fleq d$.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We demonstrate a method for finding the decoherence-subalgebra $\mathcal{N}(\mathcal{T})$ of a Gaussian quantum Markov semigroup on the von Neumann algebra $\mathcal{B}(\Gamma(\mathbb{C}^d))$ of all bounded operator on the Fock space $\Gamma(\mathbb{C}^d)$ on $\mathbb{C}^d$. We show that $\mathcal{N}(\mathcal{T})$ is a type I von Neumann algebra $L^\infty(\mathbb{R}^{d_c};\mathbb{C})\bar{\otimes}\mathcal{B}(\Gamma(\mathbb{C}^{d_f}))$ determined, up to unitary equivalence, by two natural numbers $d_c,d_f\leq d$. This result is illustrated by some applications and examples.

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