Distinguishing between statistical and systematic errors in quantum process tomography

TL;DR

This paper presents a test to distinguish statistical errors from systematic errors in quantum process tomography, crucial for correctly interpreting non-completely positive maps reconstructed from experimental data.

Contribution

The paper introduces a novel test for differentiating statistical and systematic errors in quantum process reconstructions, validated through experiments with trapped ions.

Findings

Initial system-environment correlations can cause negative eigenvalues in reconstructed maps

The proposed test effectively identifies the nature of errors in quantum process data

Experimental validation demonstrates the test's practical applicability

Abstract

It is generally assumed that every process in quantum physics can be described mathematically by a completely positive map. However, experimentally reconstructed processes are not necessarily completely positive due to statistical or systematic errors. In this paper, we introduce a test for discriminating statistical from systematic errors which is necessary to interpret experimentally reconstructed, non-completely positive maps.Wedemonstrate the significance of the test using several examples given by experiments and simulations. In particular, we demonstrate experimentally how an initial correlation between the system to be measured and its environment leads to an experimentally reconstructed map with negative eigenvalues. These experiments are carried out using atomic 171Yb+ ions confined in a linear Paul trap, addressed and coherently manipulated by radio frequency radiation.