Related papers: Another quantum version of Sanov theorem
We present a quantum extension of a version of Sanov's theorem focussing on a hypothesis testing aspect of the theorem: There exists a sequence of typical subspaces for a given set $\Psi$ of stationary quantum product states asymptotically…
We report a proof of the quantum Sanov Theorem by elementary application of basic facts about representations of the symmetric group, together with a complete characterization of the optimal error exponent in a situation where the null…
We consider Bayesian multiple hypothesis problem with independent and identically distributed observations. The classical, Sanov's theorem-based, analysis of the error probability allows one to characterize the best achievable error…
In this paper we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov's theorem for the empirical measure associated to finite sequences of…
The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical…
Nyquist-Shannon sampling theorem, instrumental in classical telecommunication technologies, is extended to quantum systems supporting a unitary representation of a finite group $G$. Two main ideas from the classical theory having natural…
Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are…
The equipartition theorem is crucial in classical statistical physics, and recent studies have revealed its quantum counterpart for specific systems. This raises the question: does a quantum counterpart of the equipartition theorem exist…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
Reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones. This is dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one. The Quantum…
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
In this work a quantum analogue of Bayesian inference is considered. Based on the notion of instrument, we propose a quantum analogue of Bayes' rule, which elaborates how a prior normal state updates under observations. Besides, we…
We identify points of difference between Invariant Set Theory and standard quantum theory, and show that these lead to noticeable differences in predictions between the two theories. We design a number of experiments to test which of these…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
Given two families of quantum states $A$ and $B$, called the null and the alternative hypotheses, quantum hypothesis testing is the task of determining whether an unknown quantum state belongs to $A$ or $B$. Mistaking $A$ for $B$ is a type…
The "marginal" distributions for measurable coordinate and spin projection is introduced. Then, the analog of the Pauli equation for spin-1/2 particle is obtained for such probability distributions instead of the usual wave functions. That…