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

Abstract

In a multiparameter estimation setting it may happen that the encoding of two or more parameters is performed by the same generator, or more generally that multiple parameters are imprinted on the probe by linearly dependent generators, then their individual values can no longer be recovered by whatever estimation scheme and we call them intertwined. A singular (quantum) Fisher information matrix characterizes this scenario. An optical example of such intertwined parameters are timedelays on a transmission line, which we might try to untwine by alternating the encoding with a beam splitter (and eventually adding an extra phase shift on one of the lines), a setup known as the generalized Hong-Ou-Mandel (GHOM) interferometry. We prove the untwining of two timedelays in the GHOM at the exclusive zero-coincidence (EZC) point, when the employed probe is the frequency-correlated biphoton state, furthermore we show the statistical independence of the two time delays and the optimality of the QFI at the EZC point. Finally we prove the compatibility of this scheme by checking the weak commutativity condition of the symmetric logarithmic derivatives.