Self-consistent quantum measurement tomography based on semidefinite programming

TL;DR

This paper introduces a semidefinite programming-based method for quantum measurement tomography that can detect experimental imperfections and perform self-consistent tomography without prior assumptions.

Contribution

It presents a novel SDP-based approach for quantum measurement tomography that enables self-consistent reconstruction of states and measurements without assuming low noise or reliable input states.

Findings

Effective detection of experimental imperfections.

Self-consistent tomography without prior assumptions.

Applicable to near-term quantum computers.

Abstract

We propose an estimation method for quantum measurement tomography (QMT) based on semidefinite programming (SDP), and discuss how it may be employed to detect experimental imperfections, such as shot noise and/or faulty preparation of the input states on near-term quantum computers. Moreover, if the positive operator-valued measure (POVM) we aim to characterize is informationally complete, we put forward a method for self-consistent tomography, i.e., for recovering a set of input states and POVM effects that is consistent with the experimental outcomes and does not assume any a priori knowledge about the input states of the tomography. Contrary to many methods that have been discussed in the literature, our approach does not rely on additional assumptions such as low noise or the existence of a reliable subset of input states.