Seminars and Workshops

Madalin Guta, University of Nottingham

Title: Local asymptotic normality in quantum statistics

Abstract: Local asymptotic normality is a key concept in mathematical statistics, which underlies the asymptotic achievability of the Cramer-Rao bound and the asymptotic normality of optimal estimators.

In this presentation, I will review some of the current progress in extending this concept to the field of quantum statistics. In quantum estimation, one is given “quantum data” in the form of a quantum system prepared in a state that depends on an unknown parameter, and would like to estimate the parameter based on “classical data” obtained by measuring the system. This raises the problem of finding optimal measurements which extract maximum amount of information about the parameter.

Quantum local asymptotic normality (QLAN) shows that in the limit of large “sample size”, certain quantum statistical models can be approximated by simpler Gaussian models where the unknown parameter is encoded linearly in the mean of the canonical variables. This simplification provides a procedures for constructing optimal estimators with normally distributed errors. I will discuss two settings in which QLAN holds: ensembles of identical, independent systems, and quantum Markov chains.

This initiative is part of the "PhD Lectures" activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.
Francesco Fidaleo, Dipartimento di Matematica, Università di Roma Tor Vergata: Spectral actions for free particles and their asymptotics, September 17, 2024. Room Aula Seminari III piano, on the third floor of building 14 (Leonardo campus, via Bonardi 9).
Sonia Mazzucchi, Dipartimento di Matematica, Università di Trento: "Certified randomness from single-particle entanglement", July 01, 2024 at 14:15. Room Aula Seminari III piano, on the third floor of building 14 (Leonardo campus, via Bonardi 9).
Vitonofrio Crismale, Dipartimento di Matematica, Università di Bari: "Distributional symmetries on CAR and CCR algebras", July 01, 2024 at 15:15. Room Aula Seminari III piano, on the third floor of building 14 (Leonardo campus, via Bonardi 9).
44th International conference on Quantum Probability and Infinite dimensional Analysis ( from May 13 to 17, 2024), BellaVista Relax Hotel, Levico Terme (TN). https://sites.google.com/view/qpida44/home-page?authuser=1
School on Quantum Probability Control and Engineering (from May 09 to 11, 2024), Politecnico di Milano. Room Sala Consiglio, on the seven floor of building 14 (Leonardo campus, via Bonardi 9). https://www.mate.polimi.it/events/QPCE/?cn-reloaded=1
Tommaso Macrì, Executive Account Manager and Quantum Expert @ QuEra Computing Inc: "QuEra: Quantum Computing with Neutral Atoms", April 10, 2024 at 11.00, Aula Alpha, Edificio 24 (Leonardo campus, via Bonardi 9). Registrazion link: https://forms.office.com/e/W2Z5240yMW
Federico Girotti (Politecnico di Milano): "An introduction to Quantum Channels and applications", February 08, 2024 at 11:45. Room Aula Seminari III piano, on the third floor of building 14 (Leonardo campus, via Bonardi 9).
QQQ Workshop on Quantum open systems, Quantum thermodynamics, Quantum probability (from February 18 to 21, 2020): https://sites.google.com/view/qqqconference/
Third Italian-Korean Symposium on Quantum Probability and Infinite Dimensional Analysis, February 17--19, 2019. Room Sala Consiglio, on the seven floor of building 14 (Leonardo campus, via Bonardi 9).
ESTIMATION AND CONTROL OF OPEN QUANTUM SYSTEMS, Institut Henri Poincaré (IHP): https://q-coast.sciencesconf.org/
43rd International Conference On Quantum Probability, and Infinite Dimensional Analysis (QP43): http://math.hanyang.ac.kr/users/math/common/2/qp43/qp43.html
Jos Uffink (University of Minnesota): “The expression of the Uncertainty Principle of Quantum Mechanics”, September 27 at 4pm. Room Aula Consiglio, on the seventh floor of building 14 (Leonardo campus, via Bonardi 9).

Seminars

Francesco Buscemi, Nagoya University
The theory of quantum statistical comparison with some applications to quantum information science
Tuesday, September 12, 2017, at 15:00
Aula Seminari III piano

Abstract

Ameur Dhahri, Chungbuk National University
Quantum markov chains and associated open quantum random walks
Tuesday, July 11, 2017, at 14:00 o'clock
Aula Seminari III piano

Abstract

Hyun Jae Yoo, Hankyong National University
Glauber dynamics on the cycles: spectral distribution of the generator
Tuesday, July 11, 2017, at 15:00 o'clock
Aula Seminari III piano

Abstract

Giuseppa Alfano, Politecnico di Torino
Finite-dimensional random matrix models for problems of information transmission
Tuesday, June 13, 2017, at 14:00
Aula Seminari III piano

Abstract

Abstract
Information theory for communication has been formally introduced right after the second world war, with two main goals: to quantify the memory needed for information storage, and to evaluate how fast a reliable information can be transmitted through a channel, under mild assumptions on its geometry and electromagnetic properties. Later on, the original formulation has been extended to acoustic and optics waves, exploited as information carriers. During last two decades, progress in circuitry synchronization, antenna miniaturization, and signal decoding speed, made possible the coordination of transmission and reception of multiple signal streams in parallel, multiplexed over either wireless or optical channels. This provided a sensible increase in the data transmission speed, and is one of the groundbreaking paradigms at the basis of UMTS, LTE, and further communications standard. In parallel to the technological evolution, mathematical models had to be developed for the communication between pairs of antenna arrays. This led to the adoption of random matrices in the wireless communication framework. So far, a matrix-valued description of all the main information-theoretic figure-of-merit has been provided. Depending on the specific application, either asymptotic (in the antenna number) or finitedimensional random matrix theory is exploited. While the former is strictly related (and borrows several tools from) to free probability, the latter mostly relied on classical results of multivariate statistics, unfortunately only useful to predict wireless systems performance up to the current (fourth) generation of mobile telephony. In the last five years, however, new invariant random matrix ensembles have been individuated, opening the road to a comprehensive performance analysis of multi-antenna wireless communications also in next-generation settings. This talk focuses on a random matrix product, characterized in, and reports on a detailed analysis of a multiantenna transmission in the foreseen 5G channel, exploiting spectral properties of the mentioned matrix product. This talk is based on some joint works with Carla Fabiana Chiasserini and Giorgio Taricco, from Department of Electronics and Telecommunications, Politecnico di Torino, and with Alessandro Nordio, from IEIIT-CNR, Torino.

Workshops

no workshops found