Related papers: Negative Probability and Uncertainty Relations
We show within a very simple framework that different measures of fluctuations lead to uncertainty relations resulting in contradictory conclusions. More specifically we focus on Tsallis and Renyi entropic uncertainty relations and we get…
Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present…
The uncertainty relation reveals the intrinsic difference between the classical world and the quantum world. We investigate the quantum uncertainty relation of quantum channel in qubit systems. Under two general measurement bases, we first…
Aiming towards a geometric description of quantum theory, we study the coherent states-induced metric on the phase space, which provides a geometric formulation of the Heisenberg uncertainty relations (both the position-momentum and the…
Covariant phase observables are obtained by defining simple conditions for mappings from the set of phase wave functions (unit vectors of the Hardy space) to the set of phase probability densities. The existence of phase probability density…
An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two {distinctive operational} scenarios. In the first scenario, by merging {two successive…
This paper deals with positivity properties for a pseudodifferential calculus, generalizing Weyl's classical quantization, and set on an infinite dimensional phase space, the Wiener space. In this frame, we show that a positive symbol does…
Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be…
Definitions and notations with historical references are given for some numerical coefficients commonly used to quantify relations among collections of objects for the purpose of expressing approximate knowledge and probabilistic reasoning.
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These…
This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
Given a narrow signal over the real line, there is a limit to the localisation of its Fourier transform. In spaces of prime dimensions, Tao derived a sharp state-independent uncertainty relation which holds for the support sizes of a pure…
This article was written for the Logic in Computer Science column in the February 2015 issue of the Bulletin of the European Association for Theoretical Computer Science. The intended audience is general computer science audience. The…
We discuss on the uncertainty relation (UR) for a closed one dimensional system (circle). In such a system, we cannot use the angle along the circle as a position variable. Otherwise we meet difficulties about the definition of the average…
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
We consider two realizations of the $\kappa$-deformed phase space obtained as a cross product algebra extension of $k$-Poincar\'{e} algebra. Two kinds of the kappa-deformed uncertainty relations are briefly discussed.