Seminars and Workshops

ABSTRACT

ABSTRACT
The statistical analysis of measurement data has become a key component of many quantum engineering experiments. As standard full state tomography becomes unfeasible for large dimensional quantum systems, one needs to exploit prior information and the sparsity properties of the experimental state in order to reduce the dimensionality of the estimation problem. In this paper we propose model selection as a general principle for finding the simplest, or most parsimonious explanation of the data, by fitting different models and choosing the estimator with the best trade-off between likelihood fit and model complexity. We apply two well established model selection methods -- the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) -- to models consising of states of fixed rank and datasets such as are currently produced in multiple ions experiments. We test the performance of AIC and BIC on randomly chosen low rank states of 4 ions, and study the dependence of the selected rank with the number of measurement repetitions for one ion states. We then apply the methods to real data from a 4 ions experiment aimed at creating a Smolin state of rank 4. The two methods indicate that the optimal model for describing the data lies between ranks 6 and 9, and the Pearson chi^2 test is applied to validate this conclusion. Additionally we find that the mean square error of the maximum likelihood estimator for pure states is close to that of the optimal over all possible measurements.

ABSTRACT

ABSTRACT
Mostreremo come sia possibile, ed in un certo senso naturale, adoperare una tecnica operatoriale mutuata dalla meccanica quantistica per analizzare la dinamica di alcuni sistemi classici. Mostreremo alcune applicazioni ai mercati azionari ed alle dinamiche di popolazioni.

ABSTRACT

ABSTRACT
I will present a class of generators of QMS which have a close relationship with its commutative restrictions, yet quantum dynamic arises from them, and are quite easy to compute. I will give a definition of Quantum entropy production rate and show its relationship to quantum detailed balance and classical entropy production rate. Il seminario rientra nelle attività del progetto FIRB 2010 Quantum Markov Semigroups and their empirical estimation.

ABSTRACT

ABSTRACT
We apply some earlier results on the classification of covariant instruments in order to clarify some aspects related to sequential measurements of conjugated observables. The results stated are valid both in the finite and infinite dimensional setting. Particular emphasis will be given, in the end, to the finite dimensional applications.

ABSTRACT

ABSTRACT
Each covariant phase space observable is determined by a unique positive trace one operator. We characterize the informational completeness of these observables in terms of the zero set of the Weyl transform of the generating operator, the relevant condition being that the zero set has dense complement. We then consider two other conditions, namely, that the zero set is of Lebesgue measure zero, or empty. We show that all three conditions are distinct, and show how they are related to approximation theorems in harmonic analysis.