Related papers: Beyond quantum Fisher information: optimal phase e…
The minimum error of unbiased parameter estimation is quantified by the quantum Fisher information in accordance to the Cram\'{e}r-Rao bound. We indicate that only superposed NOON states by simultaneous measurements can achieve the maximum…
We propose a quantum metrology protocol based on a two-step joint evolution of the probe system and an ancillary qubit and quantum measurement. With a proper initial state of the ancillary qubit and an optimized evolution time, the quantum…
Training-free conditional diffusion models have received great attention in conditional image generation tasks. However, they require a computationally expensive conditional score estimator to let the intermediate results of each step in…
Photon counting measurement has been regarded as the optimal measurement scheme for phase estimation in the squeezed-state interferometry, since the classical Fisher information equals to the quantum Fisher information and scales as…
We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the…
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…
The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…
We present an optimal strategy having finite outcomes for estimating a single parameter of the displacement operator on an arbitrary finite dimensional system using a finite number of identical samples. Assuming the uniform {\it a priori}…
Quantum phase estimation is one of the most important tools in quantum algorithms. It can be made non-adaptive (meaning all applications of the unitary $U_\phi$ happen simultaneously) without using more applications of $U_\phi$, albeit at…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
We show how to verify the metrological usefulness of quantum states based on the expectation values of an arbitrarily chosen set of observables. In particular, we estimate the quantum Fisher information as a figure of merit of metrological…
Quantum Fisher information characterizes the phase sensitivity of qubits in the spin-boson model with a finite bandwidth spectrum. In contrast with Markovian reservoirs, the quantum Fisher information will flow from the environments to…
Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…
Phase estimation protocols provide a fundamental benchmark for the field of quantum metrology. The latter represents one of the most relevant applications of quantum theory, potentially enabling the capability of measuring unknown physical…
Quantum measurements, alongside quantum states and processes, form a cornerstone of quantum information processing. However, unlike states and processes, their efficient characterisation remains relatively unexplored. We resolve this…
In this contribution, quantum Fisher information is utilized to estimate the parameters of a central qubit interacting with a single-spin qubit. The effect of the longitudinal, transverse and the rotating strengths of the magnetic field on…
We consider the probability by which quantum phase measurements of a given precision can be done successfully. The least upper bound of this probability is derived and the associated optimal state vectors are determined. The probability…
The Fisher information matrix (FIM) is a key quantity in statistics as it is required for example for evaluating asymptotic precisions of parameter estimates, for computing test statistics or asymptotic distributions in statistical testing,…
We show that quantification of the performance of quantum-enhanced measurement schemes based on the concept of quantum Fisher information yields asymptotically equivalent results as the rigorous Bayesian approach, provided generic…
We identify optimal measurement strategies for phase estimation in different scenarios. For pure states of a single qubit, we show that optimal measurements form a broad set parametrized with a continuous variable. When the state is mixed…