Related papers: Quantum Limits on Parameter Estimation
We introduce quantum parameter estimation with the encoding being via a quantum measurement. We quantify the precision for estimating parameters characterizing a general two-outcome qubit measurement, considering two cases: when the…
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…
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 metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a…
We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean-square errors when estimating relevant parameters with separable…
We consider the problem of quantum phase estimation with access to arbitrary measurements in a single suboptimal basis. The achievable sensitivity limit in this case is determined by the classical Cram\'{e}r-Rao bound with respect to the…
The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical…
Quantum metrology protocols are typically designed around the assumption that we have an abundance of measurement data, but recent practical applications are increasingly driving interest in cases with very limited data. In this regime the…
We point out a general framework that encompasses most cases in which quantum effects enable an increase in precision when estimating a parameter (quantum metrology). The typical quantum precision-enhancement is of the order of the square…
In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…
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…
This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…
This review aims at gathering the most relevant quantum multi-parameter estimation methods that go beyond the direct use of the Quantum Fisher Information concept. We discuss in detail the Holevo Cram\'er-Rao bound, the Quantum Local…
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…
A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…
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…
The Cram\'er-Rao bound captures completely the performance of single-parameter quantum sensors. On the other hand, its extension to multiple parameters demands more caution. Different aspects need to be captured at once, including,…
The quantum Cram\'er-Rao (QCR) bound sets the ultimate local precision limit for unbiased multiparameter estimation. Yet, unlike in the single-parameter case, its saturability is not generally guaranteed and is often assessed through…
For decoherence processes induced by weak interactions with the environment, a general quantum channel with one noise parameter has been formulated. This channel is called low-noise channel and very useful for investigating the parameter…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…