Related papers: Bayesian Nagaoka-Hayashi Bound for Multiparameter …

The Cram\'er-Rao bound serves as a crucial lower limit for the mean squared error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing…

Achievability in information theory refers to demonstrating a coding strategy that accomplishes a prescribed performance benchmark for the underlying task. In quantum information theory, the crafted Hayashi-Nagaoka operator inequality is an…

Only with the simultaneous estimation of multiple parameters are the quantum aspects of metrology fully revealed. This is due to the incompatibility of observables. The fundamental bound for multi-parameter quantum estimation is the Holevo…

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively…

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…

This post is the author's doctoral dissertation back in 1997. The dissertation covers following four kinds of problems: First, it studies achievable Cramer-Rao type bounds of various multi-parameter pure state models. Second, it relates…

Many optimization methods for training variational quantum algorithms are based on estimating gradients of the cost function. Due to the statistical nature of quantum measurements, this estimation requires many circuit evaluations, which is…

We introduce a Bayesian method for the estimation of single qubit errors in quantum devices, and use it to characterize these errors on three 27-qubit superconducting qubit devices. We self-consistently estimate up to seven parameters of…

We prove concentration bounds for the following classes of quantum states: (i) output states of shallow quantum circuits, answering an open question from [DPMRF22]; (ii) injective matrix product states; (iii) output states of dense…

Fast and precise characterization of Gaussian states is crucial for their effective use in quantum technologies. In this work, we apply a multi-parameter moment-based estimation method that enables rapid and accurate determination of…

We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q^p of Q, as it is for example…

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…

Quantum Cram\'er--Rao theory is intrinsically local: it bounds precision near a specified parameter value, and its saturating measurement generally depends on that value. Barankin-type bounds use finite parameter displacements, but remain…

Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not…

The Holevo bound is a keystone in many applications of quantum information theory. We propose "weak maximal Holevo quantity" with weak measurements as the generalization of the standard Holevo quantity which is defined as the optimal…

We find a large class of pure and mixed input states with which the phase estimation precision saturates the Cramer-Rao bound under the compound measurements of parity and particle number. We further propose a quantum-phase-estimation…

Quantum phase estimation based on Gaussian states plays a crucial role in many application fields. In this paper, we study the precision bound for the scheme using two-mode squeezed Gaussian states. The quantum Fisher information is…

In this work, we study the phase estimation problem. We show an alternative, simpler and self-contained proof of query lower bounds. Technically, compared to the previous proofs [NW99, Bes05], our proof is considerably elementary.…

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the…

A new version of random phase approximation is proposed for low-energy harmonic vibrations in nuclei. The theory is not based on the quasi-particle vacuum of the BCS/HFB ground state, but on the pair condensate determined in Ref. [4]. The…