We are in the midst of a second quantum revolution fueled by &ldquo\;qua ntumness&rdquo\; of physical systems and the sophisticated measurement dev ices or detectors to produce and characterize these exotic systems. Thus\, characterization of quantum states and the detectors is a key task in opt ical quantum science and technology. The Wigner quasi-probability distribu tion function provides such a characterization. In this talk\, I present o ur recent results on quantum state tomography of a single-photon Fock stat e using photon-number-resolving measurements using superconducting transit ion-edge sensor [1]. We directly probe the negativity of the Wigner functi on in our raw data without any inference or correction for decoherence\, w hich is also an important indicator of the &ldquo\;quantum-only&rdquo\; na ture of a physical system. For the second part of the talk\, we discuss a method to characterize quantum detectors by experimentally identifying the Wigner functions of the detector positive-operator-value-measures (POVMs) \, a set of hermitian operators completely describing the detector [2]. Th e proposed scheme uses readily available thermal mixtures and probes the W igner function point-by-point over the entire phase space from the detecto r&rsquo\;s outcome statistics. In order to make the reconstruction robust to the experimental noise\, we use techniques from convex quadratic optimi zations.

\n\nReferences

\n1. R. Nehra\, A. Win\,
M. Eaton\, R. Shahrokhshahi\, N. Sridhar\, T. Gerrits\,A. Lita\, S. W. Nam
\, and O. Pﬁ\;ster\, &ldquo\;State-independent quantum state tomogra
phy by photon-number-resolving measurements\,&rdquo\; Optica 6\,1356&ndash
\;1360 (2019). 2. R. Nehra and K. Valson Jacob (2019)\, &ldquo\;Characteri
zing quantum detectors by Wigner functions\,&rdquo\; [arXiv:1909.10628].**\n \;**