Direct state reconstruction with coupling-deformed pointer observables

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 $\mathbf{\text{93}}$, 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.