Related papers: Quantum ensembles and the statistical operator: a …
Quantum classification is defined as the task of predicting the associated class of an unknown quantum state drawn from an ensemble of pure states given a finite number of copies of this state. By recasting the state discrimination problem…
It is proposed to define "quantumness" of a system (micro or macroscopic, physical, biological, social, political) by starting with understanding that quantum mechanics is a statistical theory. It says us only about probability…
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the…
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail)…
One attractive interpretation of quantum mechanics is the ensemble interpretation, where Quantum Mechanics merely describes a statistical ensemble of objects and not individual objects. But this interpretation does not address why the…
Producing quantum states at random has become increasingly important in modern quantum science, with applications both theoretical and practical. In particular, ensembles of such randomly-distributed, but pure, quantum states underly our…
Recently, there has been a growing literature exploring the generalization of quantum algorithms, such that different quantum algorithms are special examples of a more fundamental structure. In this short paper, we provide a general…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
A goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. Such intrusion is usually seen to arise because observation somehow selects a single actuality from among…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
Quantum state discrimination is a fundamental concept in quantum information theory, which refers to a class of techniques to identify a specific quantum state through a positive operator-valued measure. In this work, we investigate how…
Deep learning has seen substantial achievements, with numerical and theoretical evidence suggesting that singularities of statistical models are considered a contributing factor to its performance. From this remarkable success of classical…
We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the…
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…
We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient…
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…
The preparation procedure, an undefined notion in quantum theory, has not had the relevance that it deserves in the interpretation of quantum mechanical formalism. Here we utilize the concepts of identical and similar preparation procedures…
Quantum simulators are devices that actively use quantum effects to answer questions about model systems and, through them, real systems. Here we expand on this definition by answering several fundamental questions about the nature and use…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…
The notion of a $U$-statistic for an $n$-tuple of identical quantum systems is introduced in analogy to the classical (commutative) case: given a selfadjoint `kernel' $K$ acting on $(\mathbb{C}^{d})^{\otimes r}$ with $r<n$, we define the…