Multiparameter Estimation in Networked Quantum Sensors

Abstract

We introduce a general model for a network of quantum sensors, and we use this model to consider the following question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or nonlinear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.

Review of Modern State of Quantum Technologies

“…Достижения в этой области позволят существенно повысить точность и разрешение измерений, а также сделать многие измерения неинвазивными. В этом направлении уже сегодня есть много практических достижений [Proctor, 2017].…”

Bounding the quantum limits of precision for phase estimation with loss and thermal noise

“…It has already found use in proving the fundamental limits of covert sensing [11]. Other potential applications of our result include finite-length analysis of channel estimation in quantum key distribution protocols [18], distributed sensing using shared entanglement [19][20][21][22][23], and other problems requiring bounding the fundamental limits of sensing an unknown parameter embedded in a correlated field. We denote operators with a circumflex (e.g.,ρ for density operators) and estimators with a tilde (e.g.,μ orθ ).…”

“…(19), is an upper bound on the QFI that accounts for thermal photons in the environment and an arbitrary input state. Our bound is a function of the number of modes n, the mean and variance of the total number of photons N S in the n-mode probe, and the channel transmissivity η and mean thermal photon number per moden B .…”

Distributed quantum sensing using continuous-variable multipartite entanglement

“…For example, when the bipartite entanglement of two-mode squeezed states is leveraged in target detection, it provides a signal-to-noise ratio advantage over that of the optimum classical scheme [4][5][6][7][8]. Prior work has shown that multipartite entanglement between distributed sensors could yield significant sensitivity enhancement in estimating the weighted sum of unknown parameters in the sensor network [9,10]. However, these distributed quantum-sensing protocols rely on photonic discrete-variable multipartite entanglement, which, to date, can only be probabilistically generated and is extremely vulnerable to environmental loss.…”

“…Before proceeding, it is worth contrasting the approach we take with recent work on distributed quantum sensing [9,10]. Reference [9]'s distributed phase sensing required twin Fock-state generation and photon-number resolving detectors to realize Heisenberg scaling, and Ref.…”