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The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables has…

Quantum Physics · Physics 2021-02-17 Jasminder S. Sidhu , Yingkai Ouyang , Earl T. Campbell , Pieter Kok

The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…

Machine Learning · Statistics 2024-09-09 Evan Scope Crafts , Xianyang Zhang , Bo Zhao

The widely used quantum Cramer-Rao bound (QCRB) sets a lower bound for the mean square error of unbiased estimators in quantum parameter estimation, however, in general QCRB is only tight in the asymptotical limit. With a limited number of…

Quantum Physics · Physics 2016-09-07 Jing Liu , Haidong Yuan

We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this…

Quantum Physics · Physics 2007-05-23 V. P. Belavkin

Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…

Quantum Physics · Physics 2026-05-19 Edward Gandar , Jesús Rubio

We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…

Quantum Physics · Physics 2008-12-18 R. D. Gill , S. Massar

Realisation of experiments even on small and medium-scale quantum computers requires an optimisation of several parameters to achieve high-fidelity operations. As the size of the quantum register increases, the characterisation of quantum…

Quantum Physics · Physics 2020-08-11 F. Martínez-García , D. Vodola , M. Müller

Multiparameter quantum estimation theory is crucial for many applications involving infinite-dimensional Gaussian quantum systems, since they can describe many physical platforms, e.g., quantum optical and optomechanical systems and atomic…

Quantum Physics · Physics 2025-04-28 Shoukang Chang , Marco G. Genoni , Francesco Albarelli

We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian…

Quantum Physics · Physics 2017-02-08 Olivier Pinel , Pu Jian , Claude Fabre , Nicolas Treps , Daniel Braun

We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian…

Quantum Physics · Physics 2015-06-16 O. Pinel , P. Jian , N. Treps , C. Fabre , and D. Braun

Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian…

Quantum Physics · Physics 2020-05-04 Joseph M. Lukens , Kody J. H. Law , Ajay Jasra , Pavel Lougovski

In this paper, we prove a quantum union bound that is relevant when performing a sequence of binary-outcome quantum measurements on a quantum state. The quantum union bound proved here involves a tunable parameter that can be optimized, and…

Quantum Physics · Physics 2019-01-11 Samad Khabbazi Oskouei , Stefano Mancini , Mark M. Wilde

Quantum bits, or qubits, are the fundamental building blocks of present quantum computers. Hence, it is important to be able to characterize the state of a qubit as accurately as possible. By evaluating the qubit characterization problem…

Quantum Physics · Physics 2024-02-27 Bacui Li , Lorcan O. Conlon , Ping Koy Lam , Syed M. Assad

We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H= \theta H_0$,…

Quantum Physics · Physics 2008-07-03 Rolando D. Somma , Sergio Boixo

The Holevo Cram\'er Rao bound is a lower bound on the sum of the mean square error of estimates for parameters of a state. We provide a method for calculating the Holevo Cram\'er-Rao bound for estimation of quadrature mean parameters of a…

Quantum Physics · Physics 2018-01-22 Mark Bradshaw , Ping Koy Lam , Syed M. Assad

A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…

Statistics Theory · Mathematics 2023-03-02 Shuo Tang , Gerald LaMountain , Tales Imbiriba , Pau Closas

This work compares the performance of single and two qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using…

Quantum Physics · Physics 2023-08-01 Lorcan. O. Conlon , Ping Koy Lam , Syed. M. Assad

We give a lower bound on the probability of error in quantum state discrimination. The bound is a weighted sum of the pairwise fidelities of the states to be distinguished.

Quantum Physics · Physics 2016-11-15 Ashley Montanaro

Bayesian error analysis paves the way to the construction of credible and plausible error regions for a point estimator obtained from a given dataset. We introduce the concept of region accuracy for error regions (a generalization of the…

Quantum Physics · Physics 2019-07-15 Changhun Oh , Yong Siah Teo , Hyunseok Jeong

Optimal measurements for quantum multiparameter estimation are complicated by the uncertainty principle. Generally, there is a trade-off between the precision with which different parameters can be simultaneously estimated. The task of…

Quantum Physics · Physics 2025-11-20 Simon K. Yung , C. M. Yung , Lorcán O. Conlon , Syed M. Assad