Related papers: Entropic uncertainty relation for mutually unbiase…
Combining measurements which have "theoretical uncertainties" is a delicate matter, due to an unclear statistical basis. We present an algorithm based on the notion that a theoretical uncertainty represents an estimate of bias.
In presence of quantum memory [M. Berta, M. Christandl, R. Colbeck, J.M. Renes, and R. Renner, Nature Phys. 6, 659 (2010)] the lower bound of entropic uncertainty relation depends on amount of entanglement between the particle (on which two…
Quantum multiparameter estimation focuses on the simultaneous inference of multiple parameters in quantum systems through measurement and data processing. Its complexity stems from two key factors: measurement incompatibility and parameter…
The uncertainty principle is an important principle in quantum theory. Based on this principle, it is impossible to predict the measurement outcomes of two incompatible observables, simultaneously. Uncertainty principle basically is…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
In this paper, we show an interesting connection between a quantum sampling technique and quantum uncertainty. Namely, we use the quantum sampling technique, introduced by Bouman and Fehr, to derive a novel entropic uncertainty relation…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic interpretation.…
Based on mixedness definition as M=1-tr(\r{ho}^2), we obtain a new variance-based uncertainty equality along with an inequality for Hermitian operators of a single-qubit system. The obtained uncertainty equality can be used as a measure of…
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…
Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.
This paper presents the uncertainty related to position and momentum localization of a quantum state in terms of entropic uncertainty relations. We slightly improve the inequality given in [Phys. Rev. A 74, 052101 (2006)] and introduce a…
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…
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum.…
Quantum uncertainty relations are typically analyzed for a pair of incompatible observables, however, the concept per se naturally extends to situations of more than two observables. In this work, we obtain tripartite quantum…
We compute R\'enyi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two-dimensional quantum systems. The relative amount of uncertainty between two states depends on the uncertainty…
The uncertainty principle, which bounds the uncertainties involved in obtaining precise outcomes for two complementary variables defining a quantum particle, is a crucial aspect in quantum mechanics. Recently, the uncertainty principle in…
We study quantum measurement retrodiction using the principle of minimum change. For quantum-to-classical measurement channels, we show that all standard quantum divergences select the same retrodictive update, yielding a unique and…