Heisenberg-limited continuous-variable distributed quantum metrology with arbitrary weights

TL;DR

This paper characterizes the structure and fundamental limits of continuous-variable distributed quantum metrology networks, demonstrating how nonclassical states enable Heisenberg-limited sensitivity for arbitrary parameter functions.

Contribution

It provides a complete analysis of linear networks with two non-vacuum inputs, establishing bounds and conditions for quantum advantage in distributed quantum metrology.

Findings

Single non-vacuum input achieves Heisenberg limit for sum estimation.

Two inputs, including classical, enable arbitrary linear function measurement.

Nonclassical states like squeezed vacuum enhance sensitivity beyond classical limits.

Abstract

Distributed quantum metrology (DQM) enables the estimation of global functions of d distributed parameters beyond the capability of separable sensors. Continuous-variable DQM involves using a linear network with at least one nonclassical input. Here we fully elucidate the structure of linear networks with two non-vacuum inputs which allows us to prove a number of fundamental properties of continuous-variable DQM. While measuring the sum of d parameters at the Heisenberg limit can be achieved with a single non-vacuum input, we show that two inputs, one of which can be classical, is required to measure an arbitrary linear combination of d parameters and an arbitrary global function of the parameters. We obtain a universal and tight upper bound on the sensitivity of DQM networks with two inputs, and completely characterize the properties of the nonclassical input required to obtain a quantum advantage. This reveals that a wide range of nonclassical states make this possible, including a squeezed vacuum. We also show that for a class of nonclassical inputs local photon number detection will achieve the maximum sensitivity. Finally we show that a general DQM network has two distinct regimes. The first achieves Heisenberg scaling. In the second the nonclassical input is much weaker than the coherent input, nevertheless providing a multiplicative enhancement to the otherwise classical sensitivity.