Quantum Probability Team
Workshops and Seminars
(for other seminars related to Quantum Information in the "Città Studi" area see also Open Systems & Quantum Information Seminars)
15 - 10 - 2018, Workshop The 39th International Conference on Quantum Probability and Infinite Dimensional Analysis
02 - 09 - 2018, Workshop Quantum Transport Equations and Applications
06 - 06 - 2018, Workshop Three Days in Quantum Mechanics
12 - 10 - 2018 ore 14:00 - Aula Seminari III piano
Louis H. Y. Chen (National University of Singapore): On the error bound in the normal approximation for Jack measures
The one?parameter family of Jack_? measures on partitions of n is an important discrete analog of Dyson’s ? ensembles of random matrix theory. Except for ? = ½, 1, 2, which have group theoretic interpretations, the Jack_ ? measure is difficult to analyze. In the case ? = 1, the Jack measure agrees with the Plancherel measure on the irreducible representations of the symmetric group S_n, parametrized by the partitions of n. The normal approximation for the character ratio evaluated at the transposition (12) under the Plancherel measure has been well studied, notably by Fulman (2005, 2006) and Shao and Su (2006). A generalization of the character ratio under the Jack_ ? measure has also been studied by Fulman (2004, 2006) and Fulman and Goldstein (2011). In this talk, we present results on both uniform and non?uniform error bounds on the normal approximation for the Jack_ ? measure for ? > 0. Our results improve those in the literature and come very close to solving a conjecture of Fulman (2004). Our proofs use Stein’s method and zero?bias coupling. This talk is based on joint work with Le Van Thanh.
13 - 02 - 2018 ore 14:30 - Aula Seminari III piano
Caterina Foti (Università degli Studi di Firenze): Macroscopic quantum systems & Measuring apparatuses
The emergence of classicality is the mechanism that makes us to observe a classical reality despite the fundamental laws of physics being quantum. Apart from the neverending diatribe between different interpretations of Quantum Mechanics, what can be considered more or less accepted is that we experience a classical reality due to the continuos interaction between each microscopic component of any physical system and its environment, that can be regarded as the measuring apparatus and must be macroscopic since it contains us as observers. Among the various approaches proposed over the years by different authors to deal with the "quantum-to-classical" crossover, a useful tool is provided by the general method introduced by L. G. Yaffe in 1982 for finding the classical limits as large-N limits of arbitrary quantum theories with N dynamical variables. Such method isolates the minimal structure that any quantum theory should possess in order to have a classical limit. By using Yaffe's results in the framework of open quantum systems dynamics, one can show that whenever quantum environments have a sensible large-N limit, they evolve as if they were the same measuring apparatus in the classical limit.