Efficient tomography with unknown detectors

Abstract

We compare the two main techniques used for estimating the state of a\nphysical system from unknown measurements: standard detector tomography and\ndata-pattern tomography. Adopting linear inversion as a fair benchmark, we show\nthat the difference between these two protocols can be traced back to the\nnonexistence of the reverse-order law for pseudoinverses. We capitalize on this\nfact to identify regimes where the data-pattern approach outperforms the\nstandard one and vice versa. We corroborate these conclusions with numerical\nsimulations of relevant examples of quantum state tomography.\n