Seminars and Workshops

ABSTRACT

ABSTRACT
In mathematical statistics a central role is played by the notion of statistical models (or, equivalently, statistical experiments). These objects, which can be imagined as families of probability distributions, are often used to describe the statistician's state of knowledge about an unknown parameter. It is then natural to compare statistical models on the basis of their "information content." This kind of problems led in the 1950s to the formulation of a whole new theory, sometimes named "statistical comparison theory," which soon developed into a very deep field with many applications, ranging from mathematical statistics, to physics and economics. In this lecture I will present an overview of the basic ideas of statistical comparison, some possible generalizations to the quantum setting, and a few applications in quantum thermodynamics, entanglement theory, quantum measurement theory, and the theory of open quantum systems.

ABSTRACT

ABSTRACT
We establish the connection between Open Quantum Random Walks and the Quantum Markov Chains. In particular, we construct tow kinds of Quantum Markov Chains associated with Open Quantum Random Walks. Finally, we study the recurrence, transience and the property of accessibility associated to these Quantum Markov Chains.

ABSTRACT

ABSTRACT
We consider Glauber dynamics on finite cycles. By introducing a vacuum state we consider an algebraic probability space for the generator of the dynamics. We obtain a quantum decomposition of the generator and construct an interacting Fock space. As a result we obtain a distribution of the generator in the vacuum state. We also discuss the monotonicity of the moments of spectral measure as the couplings increase. In particular, when the couplings are assumed to be uniform, as the cycle grows to an infinite chain, we show that the distribution (under suitable dilation and translation) converges to a Kesten distribution.

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.