Related papers: Measurement incompatibility in Bayesian multiparam…

We investigate the measurement incompatibility of continuous-variable systems with infinite-dimensional Hilbert spaces under the influence of pure losses, a fundamental noise source in quantum optics, and a significant challenge for…

We investigate critical quantum metrology,that is the estimation of parameters in many-body systems close to a quantum critical point, through the lens of Bayesian inference theory. We first derive a no-go result stating that any…

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…

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

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,…

In contrast with classical physics, in quantum physics some sets of measurements are incompatible in the sense that they can not be performed simultaneously. Among other applications, incompatibility allows for contextuality and Bell…

We present a joint-measurement uncertainty relation for a pair of mean square deviations of canonical variables averaged over Gaussian distributed quantum optical states. Our Bayesian formulation is free from the unbiasedness assumption,…

The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…

Some quantum measurements can not be performed simultaneously, i.e. they are incompatible. Here we show that every set of incompatible measurements provides an advantage over compatible ones in a suitably chosen quantum state discrimination…

Fidelity is the standard measure for quantifying the similarity between two quantum states. It is equal to the square of the minimum Bhattacharyya coefficient between the probability distributions induced by quantum measurements on the two…

A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…

Multiparameter quantum estimation faces a fundamental challenge due to the inherent incompatibility of optimal measurements for different parameters, a direct consequence of quantum non-commutativity. This incompatibility is quantified by…

Optical phase measurement is a simple example of a quantum--limited measurement problem with important applications in metrology such as gravitational wave detection. The formulation of optimal strategies for such measurements is an…

The concept of compatibility originally emerged as a synonym for the commutativity of observables and later evolved into the notion of measurement compatibility. In any case, however, it has remained predominantly algebraic in nature, tied…

The existence of incompatible measurements is a fundamental phenomenon having no explanation in classical physics. Intuitively, one considers given measurements to be incompatible within a framework of a physical theory, if their…

We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the…

It is well known that when two or more quantum measurements suffer from imperfections they may lose their incompatibility. For a quantum system of finite dimension d we study the incompatibility of all projective measurements subjected to…

We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account,…

We introduce a new way of quantifying the degrees of incompatibility of two ob- servables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all…