Related papers: Evaluating the quantum optimal biased bound in a u…
Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cram\'{e}r-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB…
Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…
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 classical Cram\'er-Rao inequality gives a lower bound for the variance of a unbiased estimator of an unknown parameter, in some statistical model of a random process. In this note we rewrite the statment and proof of the bound using…
Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or that of low signal-to-noise ratios, the meaning of common frequentist…
Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact…
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…
In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
Quantum discrimination and estimation are pivotal for many quantum technologies, and their performance depends on the optimal choice of probe state and measurement. Here we show that their performance can be further improved by suitably…
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,…
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 propose a phase-difference estimation algorithm based on the tensor-network circuit compression, leveraging time-evolution data to pursue scalability and higher accuracy on a quantum phase estimation (QPE)-type algorithm. Using tensor…
In many practical parameter estimation problems, such as coefficient estimation of polynomial regression, the true model is unknown and thus, a model selection step is performed prior to estimation. The data-based model selection step…
We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum…
The theoretical foundation of quantum sensing is rooted in the Cram\'er-Rao formalism, which establishes quantitative precision bounds for a given quantum probe. In many practical scenarios, where more than one parameter is unknown, the…
In the SU(2) dynamics, it is especially significant to achieve a simultaneous optimal multiparameter estimation but it is very difficult. Evolution on SU(N) dynamics is a research method to explore simultaneous multiparameter estimation…
In many estimation theory and statistical analysis problems, the true data model is unknown, or partially unknown. To describe the model generating the data, parameterized models of some degree are used. A question that arises is which…
Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…
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…