Self-consistent state and measurement tomography with fewer measurements

TL;DR

This paper introduces a method for efficiently characterizing a single qubit's state and measurement apparatus using only ten measurements, with high accuracy demonstrated through experimental reconstructions.

Contribution

The authors present a self-consistent tomography technique that requires fewer measurements and minimal assumptions, improving efficiency in quantum state and measurement characterization.

Findings

95% of reconstructed POVMs have fidelities ≥ 0.98

92% of density operators have fidelities ≥ 0.98

Method successfully reconstructs over 300 state-measurement pairs

Abstract

We describe a technique for self consistently characterizing both the quantum state of a single qubit system, and the positive-operator-valued measure (POVM) that describes measurements on the system. The method works with only ten measurements. We assume that a series of unitary transformations performed on the quantum state are fully known, while making minimal assumptions about both the density operator of the state and the POVM. The technique returns maximum-likely estimates of both the density operator and the POVM. To experimentally demonstrate the method, we perform reconstructions of over 300 state-measurement pairs and compare them to their expected density operators and POVMs. We find that 95% of the reconstructed POVMs have fidelities of 0.98 or greater, and 92% of the density operators have fidelities that are 0.98 or greater.