Related papers: Stochastic Processes: From Classical to Quantum
Of indisputable relevance for non-equilibrium thermodynamics, fluctuations theorems have been generalized to the framework of quantum thermodynamics, with the notion of work playing a key role in such contexts. The typical approach consists…
These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…
Stochastic semiclassical gravity of the 90's is a theory naturally evolved from semiclassical gravity of the 70's and 80's. It improves on the semiclassical Einstein equation with source given by the expectation value of the stress-energy…
We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective…
Stochastic mechanics (SM), as proposed by Edward Nelson and others in the 20th century, aims to reconstruct quantum mechanics (QM) from a more fundamental theory of classical point particles interacting with a classical-like ether, where…
Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…
We deal with the general structure of (noncommutative) stochastic processes by using the standard techniques of Operator Algebras. Any stochastic process is associated to a state on a universal object, i.e. the free product $C^*$-algebra in…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker-Plank-Smoluchowski equation models the time evolution of the…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
In order to understand the source and extent of the greater-than-classical information processing power of quantum systems, one wants to characterize both classical and quantum mechanics as points in a broader space of possible theories.…
Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical mechanics. Our main…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
The fundamental problem of the transition from quantum to classical physics is usually explained by decoherence, and viewed as a gradual process. The study of entanglement, or quantum correlations, in noisy quantum computers implies that in…
The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information…
In this thesis, I present several results on quantum statistical inference in the following two directions. Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on…
The initial time-dependence of a state in circumstances where it makes transitions to, or decay to, a second state has been investigated. In classical stochastic processes, the observed time dependence of transition or decay proportional to…