Related papers: Conciliation of Bayes and Pointwise Quantum State …
We revisit the problem of estimating an unknown parameter of a pure quantum state, and investigate `null-measurement' strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state.…
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…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
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,…
In this work we propose a Bayesian version of the Nagaoka-Hayashi bound when estimating a parametric family of quantum states. This lower bound is a generalization of a recently proposed bound for point estimation to Bayesian estimation. We…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
We experimentally analyzed the statistical errors in quantum-state estimation and examined whether their lower bound, which is derived from the Cramer-Rao inequality, can be truly attained or not. In the experiments, polarization states of…
A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we…
We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…
The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the…
We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most…
We derived an asymptotic bound the accuracy of the estimation when we use the quantum correlation in the measuring apparatus. It is also proved that this bound can be achieved in any model in the quantum two-level system. Moreover, we show…
The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the…
We address the use of asymptotic incompatibility (AI) to assess the quantumness of a multiparameter quantum statistical model. AI is a recently introduced measure which quantifies the difference between the Holevo and the SLD scalar bounds,…
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 report our theoretical and experimental investigations into errors in quantum state estimation, putting a special emphasis on their asymptotic behavior. Tomographic measurements and maximum likelihood estimation are used for estimating…
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…
In a unified viewpoint in quantum channel estimation, we compare the Cramer-Rao and the mini-max approaches, which gives the Bayesian bound in the group covariant model. For this purpose, we introduce the local asymptotic mini-max bound,…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
We derive lower bounds on the Bayes risk in decentralized estimation, where the estimator does not have direct access to the random samples generated conditionally on the random parameter of interest, but only to the data received from…