Related papers: Global Bounds beyond Local Quantum Metrology
In location estimation, we are given $n$ samples from a known distribution $f$ shifted by an unknown translation $\lambda$, and want to estimate $\lambda$ as precisely as possible. Asymptotically, the maximum likelihood estimate achieves…
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,…
Quantum Annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for…
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…
We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is…
In this note an intrinsic version of the Cram\'er-Rao bound on estimation accuracy is established on the Special Orthogonal group $SO(3)$. It is intrinsic in the sense that it does not rely on a specific choice of coordinates on $SO(3)$:…
In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…
We study the notion of a generalization bound being uniformly tight, meaning that the difference between the bound and the population loss is small for all learning algorithms and all population distributions. Numerous generalization bounds…
Continuous monitoring of driven-dissipative quantum optical systems is a crucial element in the implementation of quantum metrology, providing essential strategies for achieving highly precise measurements beyond the classical limit. In…
Information geometry describes a framework where probability densities can be viewed as differential geometry structures. This approach has shown that the geometry in the space of probability distributions that are parameterized by their…
The relative $\alpha$-entropy is the R\'enyi analog of relative entropy and arises prominently in information-theoretic problems. Recent information geometric investigations on this quantity have enabled the generalization of the…
We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\'er-Rao bound, although it does not require the differentiability of the model.…
Nonlocality, which is the key feature of quantum theory, has been linked with the uncertainty principle by fine-grained uncertainty relations, by considering combinations of outcomes for different measurements. However, this approach…
This tutorial gives a concise overview of existing PAC-Bayesian theory focusing on three generalization bounds. The first is an Occam bound which handles rules with finite precision parameters and which states that generalization loss is…
Quantum correlations are the singular, defining resource of quantum information science and metrology, forming the basis of every operational advantage that quantum systems hold over classical ones. Yet exact bounds on these…
We derive bounds on general quantum error correcting codes against the displacement noise channel. The bounds limit the distances attainable by codes and also apply in an approximate setting. Our main result is a quantum analogue of the…
Understanding the generalization behavior of deep neural networks remains a fundamental challenge in modern statistical learning theory. Among existing approaches, PAC-Bayesian norm-based bounds have demonstrated particular promise due to…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
Recently, a widely-used computation expression for quantum Fisher information was shown to be discontinuous at the parameter points where the rank of the parametric density operator changes. The quantum Cram\'er-Rao bound can be violated on…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…