Related papers: Multiparameter Heisenberg limit
We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large…
Quantum effects like entanglement and coherent amplification can be used to drastically enhance the accuracy of quantum parameter estimation beyond classical limits. However, challenges such as decoherence and time-dependent errors hinder…
This paper studies quantum limits to dynamical sensors in the presence of decoherence. A modified purification approach is used to obtain tighter quantum detection and estimation error bounds for optical phase sensing and optomechanical…
In the accompanying paper of arXiv:2505.00697, we have presented a generalized scheme of adaptive quantum gradient estimation (QGE) algorithm, and further proposed two practical variants which not only achieve doubly quantum enhancement in…
We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H= \theta H_0$,…
We explored the general characteristics of a Sagnac interferometer in a multiparameter estimation process. We find that in the two-parameter estimation scenario, one cannot make both parameter measurement results reach the Heisenberg limit…
This review aims at gathering the most relevant quantum multi-parameter estimation methods that go beyond the direct use of the Quantum Fisher Information concept. We discuss in detail the Holevo Cram\'er-Rao bound, the Quantum Local…
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…
The multivariate errors-in-variables regression model is applicable when both dependent and independent variables in a multivariate regression are subject to measurement errors. In such a scenario it is long established that the traditional…
We study Heisenberg scaling of quantum metrology in the viewpoint of population coding. Although Fisher information has been used for a figure of merit to characterize Heisenberg scaling in quantum metrology, several studies pointed out it…
We study the evolution of a quantum particle interacting with a random potential in the low density limit (Boltzmann-Grad). The phase space density of the quantum evolution defined through the Husimi function converges weakly to a linear…
Single parameter estimation is known to benefit from extreme sensitivity to parameter changes in quantum critical systems. However, the simultaneous estimation of multiple parameters is generally limited due to the incompatibility arising…
A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are…
Multiparameter quantum estimation theory aims to determine simultaneously the ultimate precision of all parameters contained in the state of a given quantum system. Determining this ultimate precision depends on the quantum Fisher…
From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, $\mean{\Delta \hat{q}^2}\mean{\Delta…
We present a new lower bound on the differential entropy rate of stationary processes whose sequences of probability density functions fulfill certain regularity conditions. This bound is obtained by showing that the gap between the…
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…
We calculate exactly the quantum mechanical, temporal Wigner quasiprobability density for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state. The Wigner function…
The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However,…
Two path interferometry with coherent states and squeezed vacuum can achieve phase sensitivities close to the Heisenberg limit when the average photon number of the squeezed vacuum is close to the average photon number of the coherent…