Direct reconstruction of the quantum density matrix by strong measurements

L. Calderaro1, G. Foletto1, D. Dequal2, G. Vallone1,3, P. Villoresi1,3
Phys. Rev. Lett. 121, 230501 (2018)

1Department of Information Engineering, University of Padova, via Gradenigo 6/B, 35131 Padova, Italy
2Matera Laser Ranging Observatory, Agenzia Spaziale Italiana, Italy
3 Istituto di Fotonica e Nanotecnologie, CNR, Padova, Italy

New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow to directly measure each matrix element of an unknown density operator and need only d+1 different couplings between the system and the measuring device, compared to d2 in the case of standard QST 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.