Heisenberg scaling precision in multi-mode distributed quantum metrology

Giovanni Gramegna, Danilo Triggiani, Paolo Facchi, Frank A. Narducci, Vincenzo Tamma

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We consider the estimation of an arbitrary parameter ϕ, such as the temperature or a magnetic field, affecting in a distributed manner the components of an arbitrary linear optical passive network, such as an integrated chip. We demonstrate that Heisenberg scaling precision (i.e. of the order of 1/N, where N is the number of probe photons) can be achieved without any iterative adaptation of the interferometer hardware and by using only a simple, single, squeezed light source and well-established homodyne measurements techniques. Furthermore, no constraint on the possible values of the parameter is needed but only a preliminary shot-noise estimation (i.e. with a precision of √N) easily achievable without any quantum resources. Indeed, such a classical knowledge of the parameter is enough to prepare a single, suitable optical stage either at the input or the output of the network to monitor with Heisenberg-limited precision any variation of the parameter to the order of 1/ √N without the need to iteratively modify such a stage.
Original languageEnglish
Article number053002
Number of pages8
JournalNew Journal of Physics
Publication statusPublished - 10 May 2021


  • quant-ph


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