Related papers: Negative probability
Recently it was introduced a negation of a probability distribution. The need for such negation arises when a knowledge-based system can use the terms like NOT HIGH, where HIGH is represented by a probability distribution (pd). For example,…
The presence of unique quantum correlations is the core of quantum information processing and general quantum theory. We address the fundamental question of how quantum correlations of a generic quantum system can be probed using…
The uncertainty principle is one of the characteristic properties of quantum theory, where it signals the incompatibility of two types of measurements. In this paper, we argue that measurements of time-of-arrival $T_x$ at position $x$ and…
In this article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a…
In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl--Heisenberg signaling in…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group.…
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a "weak-measurement", this disturbance can be reduced. One…
Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…
The uncertainty principle is fundamentally rooted in the algebraic asymmetry between observables. We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry, where incompatibility is quantified by an…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the…
The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The…
Given a mixture between two populations of coins, "positive" coins that each have -- unknown and potentially different -- bias $\geq\frac{1}{2}+\Delta$ and "negative" coins with bias $\leq\frac{1}{2}-\Delta$, we consider the task of…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum state tomography. We theoretically propose and experimentally…
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of…
With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…