arXiv subjects

Veronica Umanità

Publications and source records attributed to Veronica Umanità.

4 recordsLinked to original sources

arXiv2026

Quantum game theory for 2 2 games: a mathematical framework

We develop a rigorous mathematical framework for quantum game theory applied to static 2x2 games, extending classical concepts to the quantum setting where players may employ arbitrary unitary operations (pure strategies) or probability measures over the continuous group SU(2) (mixed strategies). The Eisert-Wilkens-Lewenstein protocol is introduced as the standard implementation of quantum 2x2 games. We prove the existence of Nash equilibria for continuous quantum mixed strategies via a fixed-point argument, generalising the classical Nash theorem to the quantum case.

quant-ph↗

arXiv2024

The Spectral Gap of a Gaussian Quantum Markovian Generator

Gaussian quantum Markov semigroups are the natural non-commutative extension of classical Ornstein-Uhlenbeck semigroups. They arise in open quantum systems of bosons where canonical non-commuting random variables of positions and momenta come into play. If there exits a faithful invariant density we explicitly compute the optimal exponential convergence rate, namely the spectral gap of the generator, in non-commutative $L^2$ spaces determined by the invariant density showing that the exact value is the lowest eigenvalue of a certain matrix determined by the diffusion and drift matrices. The spectral gap turns out to depend on the non-commutative $L^2$ space considered, whether the one determined by the so-called GNS or KMS multiplication by the square root of the invariant density. In the first case, it is strictly positive if and only if there is the maximum number of linearly independent noises. While, we exhibit explicit examples in which it is strictly positive only with KMS multiplication. We do not assume any symmetry or quantum detailed balance condition with respect to the invariant density.

math.FA↗

arXiv2021

The general structure of the Decoherence-free subalgebra for uniformly continuous Quantum Markov semigroups

By using the decomposition of the decoherence-free subalgebra N(T) in direct integrals of factors, we obtain a structure theorem for every uniformly continuous QMSs. Moreover we prove that, when there exists a faithful normal invariant state, N(T) has to be atomic and decoherence takes place.

quant-ph↗

arXiv2007

Relations between convergence rates in Schatten p-norms

In quantum estimation theory and quantum tomography, the quantum state obtained by sampling converges to the `true' unknown density matrix under topologies that are different from the natural notion of distance in the space of quantum states, i.e. the trace class norm. In this paper, we address such problem, finding relations between the rates of convergence in the Schatten $p$-norms and in the trace class norm.

quant-ph↗