Joint Quantum-State and Measurement Tomography with Incomplete Measurements

TL;DR

This paper introduces a joint quantum-state and measurement tomography method that reduces systematic errors by using high-fidelity preparations and limited operations, demonstrated on simulated trapped ion data.

Contribution

It presents a novel procedure for simultaneous quantum state and measurement characterization that mitigates systematic errors with minimal assumptions.

Findings

Effective in reducing systematic errors in quantum tomography

Can handle non-uniqueness by bounding state expectations

Validated through simulated trapped ion experiments

Abstract

Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by imperfect knowledge of the system. We present a procedure to simultaneously characterize quantum states and measurements that mitigates systematic errors by use of a single high-fidelity state preparation and a limited set of high-fidelity unitary operations. Such states and operations are typical of many state-of-the-art systems. For this situation we design a set of experiments and an optimization algorithm that alternates between maximizing the likelihood with respect to the states and measurements to produce estimates of each. In some cases, the procedure does not enable unique estimation of the states. For these cases, we show how one may identify a set of density matrices compatible with the measurements and use a semi-definite program to place bounds on the state's expectation values. We demonstrate the procedure on data from a simulated experiment with two trapped ions.