Julián Agredo | Searcharxiv

arXiv2025

The Kossakowski Matrix and Strict Positivity of Markovian Quantum Dynamics

We investigate the relationship between strict positivity of the Kossakowski matrix, irreducibility and positivity improvement properties of Markovian Quantum Dynamics. We show that for a Gaussian quantum dynamical semigroup strict positivity of the Kossakowski matrix implies irreducibility and, with an additional technical assumption, that the support of any initial state is the whole space for any positive time.

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arXiv2022

The decoherence-free subalgebra of Gaussian Quantum Markov Semigroups

We demonstrate a method for finding the decoherence-subalgebra $\mathcal{N}(\mathcal{T})$ of a Gaussian quantum Markov semigroup on the von Neumann algebra $\mathcal{B}(Γ(\mathbb{C}^d))$ of all bounded operator on the Fock space $Γ(\mathbb{C}^d)$ on $\mathbb{C}^d$. We show that $\mathcal{N}(\mathcal{T})$ is a type I von Neumann algebra $L^\infty(\mathbb{R}^{d_c};\mathbb{C})\bar{\otimes}\mathcal{B}(Γ(\mathbb{C}^{d_f}))$ 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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