Related papers: Distances between States and between Predicates
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
We argue that analysing schemes for metrology solely in terms of the average particle number can obscure the number of particles effectively used in informative events. For a number of states we demonstrate that, in both frequentist and…
The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…
We characterize the jammed state structure of the random sequential adsorption of segments of two different sizes on a line. To this end, we define the size ratio as a dimensionless quantity measuring the length of the large segments in…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
An expression is proposed for the quantum mechanical state of a pre- and post-selected ensemble, which is an ensemble determined by the final as well as the initial state of the quantum systems involved. It is shown that the probabilities…
We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
The colloquial phrase "partisan bias" encompasses multiple distinct conceptions of bias, including partisan advantage, packing & cracking, and partisan symmetry. All are useful and have their place, and there are several proposed measures…
We discuss the concept of connection states (or connection matrices) that describe posterior ensembles, post-selected according to the outcomes of a quantum measurement. Connection matrices allow one to obtain results of any weak and some…
In this paper we present the two-state vector formalism of quantum mechanics. It is a time-symmetrized approach to standard quantum theory particularly helpful for the analysis of experiments performed on pre- and post-selected ensembles.…
In this paper we study the Minimum Error Discrimination problem (MED) for ensembles of linearly independent (LI) states. We define a bijective map from the set of those ensembles to itself and we show that the Pretty Good Measurement (PGM)…
We uncover new features of generalized contextuality by connecting it to the Kirkwood-Dirac (KD) quasiprobability distribution. Quantum states can be represented by KD distributions, which take values in the complex unit disc. Only for…
Duality theorems play a fundamental role in convex optimization. Recently, it was shown how duality theorems for countable probability distributions and finite-dimensional quantum states can be leveraged for building relatively complete…
In the experiments considered here, we measure the y-component of momentum for a particle passing through a system of slits. The source-slit system is the preparation apparatus that determines the state vector. Recognizing that a system of…
When can a majority of voters find common ground, that is, a position they all agree upon? How does the shape of the political spectrum influence the outcome? When mathematical objects have a social interpretation, the associated theorems…
Folklore suggests that policy gradient can be more robust to misspecification than its relative, approximate policy iteration. This paper studies the case of state-aggregated representations, where the state space is partitioned and either…
The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed…
We analyze time-of-arrival probability distributions for relativistic particles in the context of quantum field theory (QFT). We show that QFT leads to a unique prediction, modulo post-selection that incorporates properties of the apparatus…
This paper studies and bounds the effects of approximating loss functions and credal sets on choice functions, under very weak assumptions. In particular, the credal set is assumed to be neither convex nor closed. The main result is that…