Direct Reconstruction of the Quantum Density Matrix by Strong Measurements

TL;DR

This paper introduces a new quantum state reconstruction method that is accurate and precise regardless of coupling strength, outperforming previous weak measurement-based techniques in experiments with single photons.

Contribution

The authors develop a non-approximated protocol for quantum state reconstruction that improves accuracy and reduces statistical errors compared to weak measurement schemes.

Findings

The new method works for all coupling strengths.

Experimental results show improved accuracy over existing methods.

The protocol reduces statistical errors in quantum state estimation.

Abstract

New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow the direct measurement of each matrix element of an unknown density operator and need only $O(d)$ different operations, compared to $d^2$ linearly independent projectors in the case of standard quantum state tomography, for the reconstruction of an arbitrary mixed state. However, due to the weakness of these couplings, these protocols are approximated and prone to large statistical errors. We propose a method which is similar to the weak measurement protocols but works regardless of the coupling strength: our protocol is not approximated and thus improves the accuracy and precision of the results with respect to weak measurement schemes. We experimentally apply it to the polarization state of single photons and compare the results to those of preexisting methods for different values of the coupling strength. Our results show that our method outperforms previous proposals in terms of accuracy and statistical errors.