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The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with…
Interference between two waves is a well-known concept in physics, and its generalization to more than two waves is straight-forward. The order of interference is defined as the number of paths that interfere in a manner that cannot be…
The Hohenberg-Mermin-Wagner (HMW) theorem states that infrared (IR) fluctuations prevent long-range order which breaks continuous symmetries in two dimensions (2D), at finite temperatures. We note that the theorem becomes physically…
This paper explores some applications of a two-moment inequality for the integral of the $r$-th power of a function, where $0 < r< 1$. The first contribution is an upper bound on the R\'{e}nyi entropy of a random vector in terms of the two…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
In a previous paper we have presented a general scheme for the implementation of symmetric generalized measurements (POVMs) on a quantum computer. This scheme is based on representation theory of groups and methods to decompose matrices…
Weak-measurement-based experiments [Kocsis et al., Science 332 (2011) 1170] have shown that, at least for pure states, the average evolution of independent photons in Young's two-slit experiment is in compliance with the trajectories…
The von Neumann interaction between a particle and an apparatus has been considered in the measurement of the position of a particle when the interaction lasts for a finite amount of time. When the measurement has finite duration, both the…
Starting with a down to earth interpretation of quantum mechanics for a free particle, the disappearance and reappearance of interference in the 2 slit problem with a detector behind one are treated in detail. A partial interpretation of…
We introduce and study the permanence properties of the class of linear transfers between probability measures. This class contains all cost minimizing mass transports, but also martingale mass transports, the Schrodinger bridge associated…
The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT…
We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…
In a seminal paper, Abbott et al. analyzed the relationship between a particle's trajectory and the resolution of position measurements performed by an observer at fixed time intervals. They predicted that quantum paths exhibit a universal…
We investigate the Wigner distributions and generalized transverse momentum-dependent distributions (GTMDs) for $u$ and $d$ quarks in the proton by using light-front quark-diquark model. We consider the contribution of scalar and…
Bohmian mechanics (BM) is a popular interpretation of quantum mechanics in which particles have real positions. The velocity of a point x in configuration space is defined as the standard probability current j(x) divided by the probability…
We discuss and experimentally demonstrate the role of quantum coherence in a sequence of two measurements collected at different times using weak measurements. For this purpose, we have realized a weak-sequential measurement protocol with…
The sliced Wasserstein metric compares probability measures on $\mathbb{R}^d$ by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and…
We study "the Wojcik model" which is a discrete-time quantum walk (QW) with one defect in one dimension, introduced by Wojcik et al.. For the Wojcik model, we give the weak convergence theorem describing the ballistic behavior of the walker…
In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…
We consider the motion of a particle under a continuum random environment whose distribution is given by the Howitt-Warren flow. In the moderate deviation regime, we establish that the quenched density of the motion of the particle (after…