Heisenberg scaling precision in multi-mode distributed quantum metrology - Giovanni Gramegna; Danilo Triggiani; Paolo Facchi; Frank A Narducci; Vincenzo Tamma (New Journal of Physics, 2021)
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 $\sqrt{N}$ ) 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 $1/\sqrt{N}$ without the need to iteratively modify such a stage.