Quantum sensing networks for the estimation of linear functions

Abstract

The theoretical framework for networked quantum sensing has been developed to a great extent in the past few years, but there are still a number of open questions. Among these, a problem of great significance, both fundamentally and for constructing efficient sensing networks, is that of the role of inter-sensor correlations in the simultaneous estimation of multiple linear functions, where the latter are taken over a collection local parameters and can thus be seen as global properties. In this work we provide a solution to this when each node is a qubit and the state of the network is sensor-symmetric. First we derive a general expression linking the amount of inter-sensor correlations and the geometry of the vectors associated with the functions, such that the asymptotic error is optimal. Using this we show that if the vectors are clustered around two special subspaces, then the optimum is achieved when the correlation strength approaches its extreme values, while there is a monotonic transition between such extremes for any other geometry. Furthermore, we demonstrate that entanglement can be detrimental for estimating non-trivial global properties, and that sometimes it is in fact irrelevant. Finally, we perform a non-asymptotic analysis of these results using a Bayesian approach, finding that the amount of correlations needed to enhance the precision crucially depends on the number of measurement data. Our results will serve as a basis to investigate how to harness correlations in networks of quantum sensors operating both in and out of the asymptotic regime.

Protocols for estimating multiple functions with quantum sensor networks: geometry and performance

“…Having made this reduction to the problem of measuring multiple linear functions in a quantum sensor network, we can connect to previous works addressing the same problem, subject to various simplifying constraints [8,10,36]. Leaving the details of these previous approaches for after we have introduced more mathematical formalism, we note that we may qualitatively divide protocols for this problem into three classes: local, global, and sequential [10].…”

Distributed quantum phase sensing for arbitrary positive and negative weights

“…The use of entanglement does not always promise a quantum enhancement in simultaneous estimation [16,19,22], but the role of entanglement becomes significant in estimating a global parameter composed of multiple parameters that are encoded across multiple modes or locations [16,23], called a distributed sensing. The most common type of a global pa-rameter having been of interest in distributed sensing is a linear combination of multiple parameters with weights [24,25]. The weights determine not only the optimal allocation of modal energies over the modes, but also the type of an optimal state.…”

Multiphase estimation without a reference mode

“…However, this focus on the single-parameter case is neither necessary nor advisable. Recent suggestions advise adopting a multiple parameter approach [15,16], thus making quantumenhanced multiparameter estimation [17][18][19][20][21][22][23][24][25][26][27][28] an important component of the next quantum revolution.…”