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Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift $\varphi$ whose generator is randomly sampled according to a…
This paper offers examples of concrete numerical applications of Bayesian quantum-state-assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior…
We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…
Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here, we investigate the joint estimation of a phase…
The estimation of multiple parameters is a ubiquitous requirement in many quantum metrology applications. However, achieving the ultimate precision limit, i.e. the quantum Cram\'er-Rao bound, becomes challenging in these scenarios compared…
In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…
An important practical problem in the field of quantum metrology and sensors is to find the optimal sequences of controls for the quantum probe that realize optimal adaptive estimation. In Belliardo et al., arXiv:2312.16985 (2023), we…
It is widely accepted that the selection of measurement bases can affect the efficiency of quantum state estimation methods, precision of estimating an unknown state can be improved significantly by simply introduce a set of symmetrical…
We find a large class of pure and mixed input states with which the phase estimation precision saturates the Cramer-Rao bound under the compound measurements of parity and particle number. We further propose a quantum-phase-estimation…
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…
The traditional framework of quantum metrology commonly assumes unlimited access to resources, overlooking resource constraints in realistic scenarios. As such, the optimal strategies therein can be infeasible in practice. Here, we…
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…
Bayesian nonparametric models offer a flexible and powerful framework for statistical model selection, enabling the adaptation of model complexity to the intricacies of diverse datasets. This survey intends to delve into the significance of…
Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…
Quantum coherence is critical resource for applications in quantum technology, among which quantum-enhanced sensing represents a typical example.Compared with quantum metrology with entangled states of multiple qubits, bosonic…
The original formulation of BEAMS - Bayesian Estimation Applied to Multiple Species - showed how to use a dataset contaminated by points of multiple underlying types to perform unbiased parameter estimation. An example is cosmological…
Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher information measurement…
The paper investigates the techniques of quantum computation in metrological predictions, with a particular emphasis on enhancing prediction potential through variational parameter estimation. The applicability of quantum simulations and…
We study the impact of many-body effects on the fundamental precision limits in quantum metrology. On the one hand such effects may lead to non-linear Hamiltonians, studied in the field of non-linear quantum metrology, while on the other…
Interferometry with quantum light is known to provide enhanced precision for estimating a single phase. However, depending on the parameters involved, the quantum limit for the simultaneous estimation of multiple parameters may not…