Direct state reconstruction with coupling-deformed pointer observables

TL;DR

This paper introduces a modified direct state tomography method using coupling-deformed pointer observables, which is valid for any measurement strength and more efficient than traditional DST, requiring fewer samples for accurate quantum state reconstruction.

Contribution

The paper proposes a new MDST scheme based on coupling-deformed pointer observables that is valid for all measurement strengths and improves efficiency over existing DST methods.

Findings

MDST is valid for measurements of any strength.

MDST requires fewer samples than DST for the same accuracy.

MDST has no inherent bias compared to DST.

Abstract

Direct state tomography (DST) using weak measurements has received wide attention. Based on the concept of coupling-deformed pointer observables presented by Zhang \emph{et al}.[Phys. Rev. A \textbf{93}, 032128 (2016)], a modified direct state tomography (MDST) is proposed, examined, and compared with other typical state tomography schemes. MDST has exact validity for measurements of any strength. We identify the strength needed to attain the highest efficiency level of MDST by using statistical theory. MDST is much more efficient than DST in the sense that far fewer samples are needed to reach DST's level of reconstruction accuracy. Moreover, MDST has no inherent bias when compared to DST.