Related papers: Comparing probability distributions: application t…
In this paper, we describe a possible generalization of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices with trace one, and to the space of matrix-valued…
The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…
Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…
Discriminating between quantum states is a fundamental problem in quantum information protocols. The optimum approach saturates the Helstrom bound, which quantifies the unavoidable error probability of mistaking one state for another.…
Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing appropriate probability distributions based on observed data is critical for…
We develop a general approach to setting up and studying classes of quantum dynamical systems close to and structurally similar to systems having specified properties, in particular detailed balance. This is done in terms of transport plans…
We establish general upper bounds on the Kolmogorov distance between two probability distributions in terms of the distance between these distributions as measured with respect to the Wasserstein or smooth Wasserstein metrics. These bounds…
Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or…
In this paper, we use the class of Wasserstein metrics to study asymptotic properties of posterior distributions. Our first goal is to provide sufficient conditions for posterior consistency. In addition to the well-known Schwartz's…
The notion of complexity of quantum states is quite different from uncertainty or information contents, and involves the tradeoff between its classical and quantum features. In this work, we we introduce a quantifier of complexity of…
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…
We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: Hilbert-Schmidt measure, Bures (statistical) measure, the measures induced by…
In classical physics the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, unidirectional transfer of population between the densely and sparsely populated…
Quantum systems are the future candidates for computers and information processing devices. Information about quantum states and processes may be incomplete and scattered in these systems. We use a quantum version of Belief Propagation(BP)…
We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem…
The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its…
The probability density quantile (pdQ) carries essential information regarding shape and tail behavior of a location-scale family. Convergence of repeated applications of the pdQ mapping to the uniform distribution is investigated and new…
We establish inequalities that compare the p-Wasserstein distance to distances which are built as suprema of box measures. More precisely, when the measures are supported on $[0,1]^d$, we obtain sharp upper-bounds of the $p$-Wasserstein…
We consider the Wigner quasi-probability distribution function of a single mode of an electromagnetic or matter-wave field to address the question of whether a direct stochastic sampling and binning of the absolute square of the complex…
The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that the distributions are supported in the same space. Recently,…