Related papers: Multiparameter Heisenberg limit
Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hybrid approach, where Hamiltonians with large amplitude are…
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2)…
The precision of quantum metrology is widely believed to be restricted by the Heisenberg limit, corresponding to a root mean square error that is inversely proportional to the number of independent processes probed in an experiment, N. In…
We study the problem of estimating the phase shift due to the general relativistic time dilation in the interference of photons using a non-linear Mach-Zender interferometer setup. By introducing two non-linear Kerr materials, one in the…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
Interferometric phase estimation is an essential tool for precise measurements of quantities such as displacement, velocity and material properties. The lower bound on measurement uncertainty achievable with classical resources is set by…
The Barankin bound is generalized to the vector case in the mean square error sense. Necessary and sufficient conditions are obtained to achieve the lower bound. To obtain the result, a simple finite dimensional real vector valued…
Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed tolerance $\delta$. The lower bound is given on the basis of…
In recent years there has been substantial development in algorithms for quantum phase estimation. In this work we provide a new approach to online Bayesian phase estimation that achieves Heisenberg limited scaling that requires…
In this work we propose a Bayesian version of the Nagaoka-Hayashi bound when estimating a parametric family of quantum states. This lower bound is a generalization of a recently proposed bound for point estimation to Bayesian estimation. We…
Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the…
The Heisenberg limit provides a quadratic improvement over the standard quantum limit, and is the maximum quantum advantage that quantum sensors could provide over classical methods. This limit remains elusive, however, because of the…
Modern precision measurements, such as interferometry for detecting gravitational waves, rely on the estimation of optical phases encoded in light fields. Here, we propose to exploit the collectively enhanced output field of a…
We consider the precision $\Delta \varphi$ with which the parameter $\varphi$, appearing in the unitary map $U_\varphi = e^{ i \varphi \Lambda}$ acting on some type of probe system, can be estimated when there is a finite amount of prior…
Entanglement is generally considered necessary for achieving the Heisenberg limit in quantum metrology. We construct analogues of Dicke and GHZ states on a single $N+1$ dimensional qudit that achieve precision equivalent to symmetrically…
In this paper the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter indexed by…
In continuous-variable quantum information processing, quantum error correction of Gaussian errors requires simultaneous estimation of both quadrature components of displacements on phase space. However, quadrature operators $x$ and $p$ are…
Sensing and imaging are among the most important applications of quantum information science. To investigate their fundamental limits and the possibility of quantum enhancements, researchers have for decades relied on the quantum…
We generalize the approach by Braunstein and Caves [Phys. Rev. Lett. 72, 3439 (1994)] to quantum multi-parameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each measurement…
We present a fully Gaussian and experimentally feasible scheme for the simultaneous estimation of the four real parameters that characterize an arbitrary two-channel unitary transformation. The scheme utilizes a two-mode squeezed probe and…