Non-Gaussian States and Measurements in Quantum Information Science

With the rapid advances in quantum information science and technology, it is of paramount importance to efficiently characterize and develop resources that are capable of offering quantum advantages. Continuous-variable quantum computation is the most scalable implementation of quantum computation to date, but it requires non-Gaussian resources to allow for exponential speedup and fault tolerance. This can be accomplished with non-Gaussian states such as Fock states or non-Gaussian measurements by photon-number-resolved detection. Therefore, it becomes a key task to devise techniques to, (a) efficiently characterize these non-Gaussian states and measurements and (b) perform non-Gaussian measurements via photon-number-resolved detection. This thesis is a step toward this goal. The work presented in this thesis is two-fold. The first part focuses on characterizing quantum states with non-Gaussian Wigner quasi-probability distribution functions using photon-number-resolving (PNR) measurements performed with the superconducting transition-edge sensor. The second part focuses on characterizing quantum detectors by Wigner functions, and designing room temperature PNR detectors using "click detectors"  such as single-photon avalanche-photodiodes (SPADs).

Within the state characterization, we first demonstrate a scheme proposed by Wallentowitz-Vogel and Banaszek-Wodkiewicz (WVBW) that allows the direct reconstruction of the Wigner function using PNR measurements. We observe the negativity of the single-photon Wigner function in the raw data without any inference or correction for decoherence. We then propose and experimentally demonstrate a novel scheme that generalizes and improves upon the WVBW scheme. The proposed scheme reconstructs the density operator, as opposed to probing the Wigner function, of an arbitrary quantum state in the Fock space from the state overlap measurements with a small set of calibrated coherent states. We devise computationally efficient and physically reliable techniques to deconvolve the deleterious effects of experimental imperfections.

In the second part of this thesis, we first investigate the feasibility and performance of a segmented waveguide detector consisting of SPADs with low dark count noise for PNR measurements. We characterize its performance by evaluating the purities of photon-count positive-operator-valued measures (POVMs) in terms of the number of SPADs, photon loss, dark counts, and electrical cross-talk. We find that the number of integrated SPADs is the dominant factor for high-quality PNR detection. Next, we propose an experimentally feasible noise-robust method to characterize a quantum detector by reconstructing the Wigner functions of the detector POVMs corresponding to the measurement outcomes.
Finally, we study a Heisenberg-limited quantum interferometer with indistinguishably photon-subtracted twin beams as an input state. We show that such an interferometer achieves Quantum Cramer-Rao bound with the intensity difference measurements and can yield a direct fringe unlike the Holland-Burnett interferometer with twin beams.