Abstract
We show a protocol achieving the ultimate Heisenberg-scaling sensitivity in the estimation of a parameter encoded in a generic linear network, without employing any auxiliary networks, and without the need of any prior information on the parameter nor on the network structure. As a result, this protocol does not require a prior coarse estimation of the parameter, nor an adaptation of the network. The scheme we analyse consists of a single-mode squeezed state and homodyne detectors in each of the M output channels of the network encoding the parameter, making it feasible for experimental applications.
Highlights
Increasing the level of precision achievable in the estimation of physical properties of systems, such as temperatures, optical lengths and magnitude of external fields among others, is one of the multiple applications of quantum technologies that have been extensively studied in the recent years
It is well known that the classical limit on the precision achievable in√the estimation of an unknown parameter when employing N probes, known as shot-noise limit, for which the error is of order 1/ N, can be surpassed by quantum strategies achieving the ultimate Heisenberg limit, where the estimation scales as 1/N [1–9]
We have shown that performing homodyne measurements at each output channel of an arbitrary linear network encoding an unknown distributed parameter φ to be estimated allows us to reach Heisenberg-scaling precision for a single-mode squeezed probe with no prior information on φ
Summary
Increasing the level of precision achievable in the estimation of physical properties of systems, such as temperatures, optical lengths and magnitude of external fields among others, is one of the multiple applications of quantum technologies that have been extensively studied in the recent years. Without making any assumption on the structure of the linear network nor on the nature of the parameter, it is always possible to reach Heisenberg-scaling sensitivity with such set-up, without the use of any auxiliary network This allows for estimation protocols not requiring a preparatory stage nor a prior coarse estimation of the parameter, as opposed to the single-channel homodyne protocols in Refs. We show that two independent contributions on the precision arise from our analysis: one originated from the presence of displaced photons in addition to squeezed photons, and the other from the squeezing of the probe We find that both contributions can reach Heisenberg-scaling sensitivity independently, and this can be achieved expectedly when the local oscillators phases are chosen such that the noise in the outcome is reduced, namely when the squeezed quadratures are observed in each output channel. This comes in useful in those cases where priority is given to increasing the precision, at the expenses of engineering an auxiliary network to be added before the estimation protocol is started
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