Related papers: On Random Unitary Channels
A reparametrization (of a continuous path) is given by a surjective weakly increasing self-map of the unit interval. We show that the monoid of reparametrizations (with respect to compositions) can be understood via ``stop-maps'' that allow…
In this paper we will develop a very general approach which shows that critical relations of holomorphic maps on the complex plane unfold transversally in a positively oriented way. We will mainly illustrate this approach to obtain…
A key problem in constrained random verification (CRV) concerns generation of input stimuli that result in good coverage of the system's runs in targeted corners of its behavior space. Existing CRV solutions however provide no formal…
Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical…
We present a method for the determination of the completely positive (CP) map describing a physical device based on random preparation of the input states, random measurements at the output, and maximum-likelihood principle. In the…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…
We study convexity of image of a general multidimensional quadratic map. We split the full image into two parts by an appropriate hyperplane such that one part is compact, and formulate a sufficient condition for convexity of the compact…
Since a quantum measurement generally disturbs the state of a quantum system, one might think that it should not be possible for a sender and receiver to communicate reliably when the receiver performs a large number of sequential…
It is now well understood that convex programming can be used to estimate the frequency components of a spectrally sparse signal from $2m+1$ uniform temporal measurements. It is conjectured that a phase transition on the success of the…
We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between $M$ quantum states that become identical under a completely decohering map. Similarly, we study distinguishability…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
Precise reconstruction of top quark properties is a challenging task at the Large Hadron Collider due to combinatorial backgrounds and missing information. We introduce a physics-informed neural network architecture called the Covariant…
Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…
We propose the use of entropy, measured from the spatial and flux distribution of pixels in the residual image, as a potential diagnostic and stopping metric for the CLEAN algorithm. Despite its broad success as the standard deconvolution…
We introduce and study two new classes of unital quantum channels. The first class describes a 2-parameter family of channels given by completely positive (CP) maps $M_3({\bf C}) \mapsto M_3({\bf C})$ which are both unital and…
We show that for various classes C of sparse graphs, and several measures of distance to such classes (such as edit distance and elimination distance), the problem of determining the distance of a given graph G to C is fixed-parameter…
We present a new class of particle methods with deformable shapes that converge in the uniform norm without requiring remappings, extended overlapping or vanishing moments for the particles. The crux of the method is to use polynomial…
This research leverages Conformal Prediction (CP) in the form of Conformal Predictive Systems (CPS) to accurately estimate uncertainty in a suite of machine learning (ML)-based radio metric models [1] as well as in a 2-D map-based ML path…
Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…