Related papers: Uncertainty Relations for Approximation and Estima…
It is shown that the well-defined unbiased measurement or disturbance of a dynamical variable is not maintained for the precise measurement of the conjugate variable, independently of uncertainty relations. The conditionally valid…
Entropic uncertainty relations are powerful tools, especially in quantum cryptography. They typically bound the amount of uncertainty a third-party adversary may hold on a measurement outcome as a result of the measurement overlap. However,…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
Number-phase uncertainty relations are formulated in terms of unified entropies which form a family of two-parametric extensions of the Shannon entropy. For two generalized measurements, unified-entropy uncertainty relations are given in…
Obtaining reliable and accurate quantification of uncertainty estimates from deep neural networks is important in safety-critical applications. A well-calibrated model should be accurate when it is certain about its prediction and indicate…
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
We investigate the uncertainty relation for estimating the position of one electron in a uniform magnetic field in the framework of the quantum estimation theory. Two kinds of momenta, canonical one and mechanical one, are used to generate…
A pair of uncertainty relations relevant for quantum states of multislit interferometry is derived, based on the mutually commuting "modular" position and momentum operators and their complementary counterparts, originally introduced by…
We present an online and data-driven uncertainty quantification method to enable the development of safe human-robot collaboration applications. Safety and risk assessment of systems are strongly correlated with the accuracy of…
We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when…
The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the…
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is…
We introduce a new technique to bound the fluctuations exhibited by a physical system, based on the Euclidean geometry of the space of observables. Through a simple unifying argument, we derive a sweeping generalization of so-called…
Entropic uncertainty relations $H(A)+H(B)\geqslant \gamma$ give a nonzero lower bound $\gamma$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the…
When making important decisions such as choosing health insurance or a school, people are often uncertain what levels of attributes will suit their true preference. After choice, they might realize that their uncertainty resulted in a…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
We prove a few novel state-dependent uncertainty relations for product as well the sum of variances of two incompatible observables. These uncertainty relations are shown to be tighter than the Roberson-Schr\"odinger uncertainty relation…