Untwining multiple parameters at the exclusive zero-coincidence points with quantum control

TL;DR

This paper demonstrates how to untwine multiple intertwined parameters in quantum estimation by using a generalized interferometric setup, achieving statistical independence and optimal information extraction at specific zero-coincidence points.

Contribution

It introduces a method to untwine intertwined parameters in quantum estimation using a GHOM interferometer and proves optimality and compatibility at the EZC point.

Findings

Parameters can be effectively untwined with a GHOM interferometer.

Optimal quantum Fisher information is achieved at the EZC point.

The scheme ensures statistical independence and compatibility of parameters.

Abstract

In this paper we address a special case of "sloppy" quantum estimation procedures which happens in the presence of intertwined parameters. A collection of parameters are said to be intertwined when their imprinting on the quantum probe that mediates the estimation procedure, is performed by a set of linearly dependent generators. Under this circumstance the individual values of the parameters can not be recovered unless one tampers with the encoding process itself. An example is presented by studying the estimation of the relative time-delays that accumulate along two parallel optical transmission lines. In this case we show that the parameters can be effectively untwined by inserting a sequence of balanced beam splitters (and eventually adding an extra phase shift on one of the lines) that couples the two lines at regular intervals in a setup that remind us a generalized Hong-Ou-Mandel (GHOM) interferometer. For the case of two time delays we prove that, when the employed probe is the frequency-correlated biphoton state, the untwining occurs in correspondence of exclusive zero-coincidence (EZC) point. Furthermore we show the statistical independence of two time delays and the optimality of the quantum Fisher information at the EZC point. Finally we prove the compatibility of this scheme by checking the weak commutativity condition associated with the symmetric logarithmic derivative operators.