Related papers: Distances between States and between Predicates
We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the…
We work in a general framework where the state of a physical system is defined by its behaviour under measurement and the global state is constrained by no-signalling conditions. We show that the marginals of symmetric states in such…
A quantum ensemble $\{(p_x, \rho_x)\}$ is a set of quantum states each occurring randomly with a given probability. Quantum ensembles are necessary to describe situations with incomplete a priori information, such as the output of a…
We describe a substructure for matter in which metric relations are not assumed as properties of a physical manifold, and instead the metric of general relativity is found in configurations of particle interactions. The 'state' of a…
The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory. However, current distance measures within the literature do not account for the direction of change between fuzzy sets; a useful concept in a…
This paper extends the asymmetric Kullback-Leibler divergence and symmetric Jensen-Shannon divergence from two probability measures to the case of two sets of probability measures. We establish some fundamental properties of these…
By combining a bound on the absolute value of the difference of mutual information between two joint probablity distributions with a fixed variational distance, and a bound on the probability of a maximal deviation in variational distance…
Lecture notes as per the title. In the first part, the concepts of a measurable space, measurable maps between measurable spaces and that of a measure on a measurable space are introduced, after which the fundamentals of the theory of…
Fidelity plays an important role in quantum information theory. In this letter, we introduce new metric of quantum states induced by fidelity, and connect it with the well-known trace metric, Sine metric and Bures metric for the qubit case.…
Typical causal effects are defined based on the marginal distribution of potential outcomes. However, many real-world applications require causal estimands involving the joint distribution of potential outcomes to enable more nuanced…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…
The indeterminism of quantum mechanics generally permits the independent specification of both an initial and a final condition on the state. Quantum pre-and-post-selection of states opens up a new, experimentally testable, sector of…
The paper introduces scaled Bregman distances of probability distributions which admit non-uniform contributions of observed events. They are introduced in a general form covering not only the distances of discrete and continuous stochastic…
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
We consider a fundamental operational task, distinguishing systems in different states, in the framework of generalized probabilistic theories and provide a general formalism of minimum-error discrimination of states in convex optimization.…
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
A family of probability distributions attached to a class of generalized weighted Bergman spaces on the Poincar\'e disk are introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained…
We consider finite irreducible Markov chains. It was shown that mean hitting time from one state to another satisfies the triangle inequality. Hence, sum of mean hitting time between couple of states in both directions is a metric on the…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…