Related papers: Quantum Sampling and Entropic Uncertainty

A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…

We examine quantum gravity effects by applying the generalized uncertainty principle (GUP) to entropic uncertainty relation conditions on quantum entanglement. In particular, we study the GUP corrections to the Shannon entropic uncertainty…

The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…

Uncertainty relation usually is one of the most important features in quantum mechanics, and is the backbone of quantum theory, which distinguishes from the rule in classical counterpart. Specifically, entropy-based uncertainty relations…

Quantum technologies promise information processing and communication technology advancements, including random number generation (RNG). Using Bell inequalities, a user of a quantum RNG hardware can certify that the values provided by an…

Let X_1, ..., X_n be a sequence of n classical random variables and consider a sample of r positions selected at random. Then, except with (exponentially in r) small probability, the min-entropy of the sample is not smaller than, roughly, a…

A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…

Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied…

The recent article "Entropic Updating of Probability and Density Matrices" [1] derives and demonstrates the inferential origins of both the standard and quantum relative entropies in unison. Operationally, the standard and quantum relative…

Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$…

We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…

Quantum Inverse Problem (QIP) is the problem of estimating an unknown quantum system $\rho$ from a set of measurements, whereas the classical counterpart is the Inverse Problem of estimating a distribution from a set of observations. In…

Given two orthornormal bases A and B, the basic form of the entropic uncertainty principle is stated in terms of the sum of the Shannon entropies of the probabilities of measuring A and B onto a given quantum state. State independent lower…

Randomness is an intrinsic feature of quantum theory. The outcome of any quantum measurement will be random, sampled from a probability distribution that is defined by the measured quantum state. The task of sampling from a prescribed…

Computational entropies provide a framework for quantifying uncertainty and randomness under computational constraints. They play a central role in classical cryptography, underpinning the analysis and construction of primitives such as…

We derive new inequalities for the probabilities of projective measurements in mutually unbiased bases of a qudit system. These inequalities lead to wider ranges of validity and tighter bounds on entropic uncertainty inequalities previously…

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…

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

In this work, we aim at augmenting the decisions output by quantum models with "error bars" that provide finite-sample coverage guarantees. Quantum models implement implicit probabilistic predictors that produce multiple random decisions…