Related papers: Ziv-Zakai Error Bounds for Quantum Parameter Estim…
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…
We present an alternative protocol allowing for the preparation of critical states that instead of suffering from the critical slowing-down benefits from the critical speeding-up. Paradoxically, we prepare these states by going away from…
I propose classical and quantum limits to the statistical resolution of two incoherent optical point sources from the perspective of minimax parameter estimation. Unlike earlier results based on the Cram\'er-Rao bound, the limits proposed…
In probabilistic quantum metrology, one aims at finding weak measurements that concentrate the Fisher Information on the resulting quantum states, post-selected according to the weak outcomes. Though the Quantum Cram\'er-Rao bound itself…
Adopting quantum resources for parameter estimation discloses the possibility to realize quantum sensors operating at a sensitivity beyond the standard quantum limit. Such approach promises to reach the fundamental Heisenberg scaling as a…
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…
Due to the potential of quantum advantage to surpass the standard quantum limit (SQL), the nonlinear interferometers have garnered significant attention from researchers in the field of precision measurement. However, many practical…
We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it requires a…
We extend the traditional framework for estimating subspace bases that maximize the preserved signal energy to additionally preserve the Cram\'er-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision…
Phase measurement constitutes a key task in many fields of science, both in the classical and quantum regime. The higher precision of such measurement offers significant advances, and can also be utilised to achieve finer estimates for…
To quantify quantum optical coherence requires both the particle- and wave-natures of light. For an ideal laser beam [1,2,3], it can be thought of roughly as the number of photons emitted consecutively into the beam with the same phase.…
We study the quantum error correction threshold of Kitaev's toric code over the group Z_d subject to a generalized bit-flip noise. This problem requires novel decoding techniques, and for this purpose we generalize the renormalization group…
Many optimization methods for training variational quantum algorithms are based on estimating gradients of the cost function. Due to the statistical nature of quantum measurements, this estimation requires many circuit evaluations, which is…
In this paper, the Cram\'{e}r-Rao Bounds (CRB) for the simultaneous estimation of power system electromechanical modes and forced oscillations (FO) are derived. Two cases are considered; in the first case only the steady-state response to…
We establish the ultimate limits that quantum theory imposes on the accuracy attainable in optical ellipsometry. We show that the standard quantum limit, as usual reached when the incident light is in a coherent state, can be surpassed with…
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…
In neutral atom quantum computers, readout and preparation of the atomic qubits are usually based on fluorescence imaging and subsequent analysis of the acquired image. For each atom site, the brightness or some comparable metric is…
The computational cost of quantum algorithms for physics and chemistry is closely linked to the spectrum of the Hamiltonian, a property that manifests in the necessary rescaling of its eigenvalues. The typical approach of using the 1-norm…
We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic…
In this paper, we employ the thoughts and methodologies of Shannon's information theory to solve the problem of the optimal radar parameter estimation. Based on a general radar system model, the \textit{a posteriori} probability density…