Related papers: Comparison of estimation limits for quantum two-pa…
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty…
In multiparameter quantum estimation, the optimal measurements for different parameters encoded in a quantum state are in general incompatible, giving rise to nontrivial tradeoffs between their attainable precisions. Understanding and…
Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…
We derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of…
Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here we resolve the conflict by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics.…
Precise measurement is crucial to science and technology. However, the rule of nature imposes various restrictions on the precision that can be achieved depending on specific methods of measurement. In particular, quantum mechanics poses…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
A fundamental challenge in multiparameter quantum estimation arises from the incompatibility of optimal measurements for different parameters, leading to intricate precision trade-offs that obscure the understanding of ultimate quantum…
Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…
We derive several expressions for the quantum Fisher information matrix (QFIM) for the multi-parameter estimation of multi-mode Gaussian quantum states, the corresponding symmetric logarithmic derivatives, and conditions for saturability of…
Critical quantum metrology relies on the extreme sensitivity of a system's eigenstates near the critical point of a quantum phase transition to Hamiltonian perturbations. This means that these eigenstates are extremely sensitive to all the…
The constrained Cramer-Rao bound (CCRB) is a lower bound on the mean-squared-error (MSE) of estimators that satisfy some unbiasedness conditions. Although the CCRB unbiasedness conditions are satisfied asymptotically by the constrained…
In this paper, we show how the Robertson uncertainty relation gives certain intrinsic quantum limits of measurements in the most general and rigorous mathematical treatment. A general lower bound for the product of the root-mean-square…
The author studies the Cram\'{e}r-Rao type bound by a linear programming approach. By this approach, he found a necessary and sufficient condition that the Cram\'{e}r-Rao type bound is attained by a random measurement. In a spin 1/2 system,…
We present a mathematical framework based on quantum interval-valued probability measures to study the effect of experimental imperfections and finite precision measurements on defining aspects of quantum mechanics such as contextuality and…
The uncertainty principle is one of the key concepts in quantum theory. This principle states that it is not possible to measure two incompatible observables simultaneously and accurately. In quantum information theory, the uncertainty…
The quantum Cram\'er-Rao bound for the joint estimation of the centroid and the separation between two incoherent point sources cannot be saturated. As such, the optimal measurements for extracting maximal information about both at the same…
A general class of Bayesian lower bounds when the underlying loss function is a Bregman divergence is demonstrated. This class can be considered as an extension of the Weinstein--Weiss family of bounds for the mean squared error and relies…
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…