Related papers: Optimal condition for measurement observable via e…
The quantum variables that can be accessed directly by experiments are described by observables. Therefore, physical parameters can only be evaluated indirectly, via estimations based on experimental measurement results. I show that the…
Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology…
In quantum metrology, it is widely believed that the quantum Cramer-Rao bound is attainable bound while it is not true. In order to clarify this point, we explain why the quantum Cramer-Rao bound cannot be attained geometrically. In this…
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
We identify precision limits for the simultaneous estimation of multiple parameters in multimode interferometers. Quantum strategies to enhance the multiparameter sensitivity are based on entanglement among particles, modes or combining…
We investigate strategies for reaching the ultimate limit on the precision of frequency estimation when the number of probes used in each run of the experiment is fixed. That limit is set by the quantum Cram\'er-Rao bound (QCRB), which…
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…
We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term…
We study the optimal way to estimate the quantum expectation value of a physical observable when a finite number of copies of a quantum pure state are presented. The optimal estimation is determined by minimizing the squared error averaged…
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A…
We study the best attainable measurement precision when a double-well trap with bosons inside acts as an interferometer to measure the energy difference of the atoms on the two sides of the trap. We introduce time independent perturbation…
We show that there exists a gap between the performance of separable and collective measurements in qubit mixed-state estimation that persists in the large sample limit. We characterize such gap in terms of the corresponding bounds on the…
The Heisenberg limit is the superior precision available by entanglement sensors. However, entanglementis fragile against dephasing, and there is no known quantum metrology protocol that can achieve Heisenberg limited sensitivity with the…
A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…
We revisit the problem of estimating an unknown parameter of a pure quantum state, and investigate `null-measurement' strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state.…
The uncertainty principle generally prohibits determination of certain pairs of quantum mechanical observables with arbitrary precision and forms the basis of indeterminacy in quantum mechanics. It was Heisenberg who used the famous…
Multimode Gaussian quantum light, including multimode squeezed and/or multipartite quadrature entangled light, is a very general and powerful quantum resource with promising applications to quantum information processing and metrology…
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems. The relations are formulated in terms of a directly operational…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
Assuming that the parameter dependent evolution, as well as the measurements that are done for readout, of a quantum system that acts as the probe in a quantum limited measurement scheme are both fixed, we find the optimal initial states of…