Related papers: Quantum Estimation by Local Observables
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all…
We discuss the problem of finding the best measurement strategy for estimating the value of a quantum system parameter. In general the optimum quantum measurement, in the sense that it maximizes the quantum Fisher information and hence…
Quantum state estimation is a fundamental task in quantum information theory, where one estimates real parameters continuously embedded in a family of quantum states. In the theory of quantum state estimation, the widely used Cram\'er Rao…
Estimating correctly the quantum phase of a physical system is a central problem in quantum parameter estimation theory due to its wide range of applications from quantum metrology to cryptography. Ideally, the optimal quantum estimator is…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally…
State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use…
As we enter the era of quantum technologies, quantum estimation theory provides an operationally motivating framework for determining high precision devices in modern technological applications. The aim of any estimation process is to…
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…
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-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum…
Many results in the quantum metrology literature use the Cram\'er-Rao bound and the Fisher information to compare different quantum estimation strategies. However, there are several assumptions that go into the construction of these tools,…
Quantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology,…
The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for…
We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias…
The quantum Cram\'er-Rao theorem states that the quantum Fisher information (QFI) bounds the best achievable precision in the estimation of a quantum parameter $\xi$. This is true, however, under the assumption that the measurement employed…
We study the optimal way to estimate the quantum expectation value of a physical observable when a finite number of copies of a quantum pure state are presented. The optimal estimation is determined by minimizing the squared error averaged…
The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cram\'er-Rao bound, which has attracted much attention in Hermitian systems since the 60s of the last century. However, less…