We investigate the capabilities of loss-tolerant quantum state characterization using a photon-number resolving, time-multiplexed detector (TMD). We employ the idea of probing the Wigner function point-by-point in phase space via photon parity measurements and displacement operations, replacing the conventional homodyne tomography. Our emphasis lies on reconstructing the Wigner function of non-Gaussian Fock states with highly negative values in a scheme that is based on a realistic experimental setup. In order to establish the concept of loss-tolerance for state characterization we show how losses can be decoupled from the impact of other experimental imperfections, i.e. the non-unity transmittance of the displacement beamsplitter and non-ideal mode overlap. We relate the experimentally accessible parameters to effective ones that are needed for an optimised state reconstruction. The feasibility of our approach is tested by Monte Carlo simulations, which provide bounds resulting from statistical errors that are due to limited data sets. Our results clearly show that high losses can be accepted for a defined parameter range, and moreover, that (in contrast to homodyne detection) mode mismatch results in a distinct signature, which can be evaluated by analysing the photon number oscillations of the displaced Fock states.
Probing information theoretic measures of nonlinear ultracold quantum gases using phase-space distributions
Sardar Vallabhbhai National Institute of Technology（萨达尔·瓦拉巴伊国家理工学院）；North Carolina State University（北卡罗来纳州立大学）；Indian Institute of Technology Bombay（孟买印度理工学院）
Wigner negativity and stellar rank for SU(1,1) states
Universidad de Guadalajara（瓜达拉哈拉大学）；Universidad Autónoma de Chile（智利自治大学）；Universidad Complutense（康普顿斯大学）；Max-Planck-Institut für die Physik des Lichts（马克斯·普朗克光科学研究所）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Université Paris Cité（巴黎西岱大学）；CNRS, Astroparticule et Cosmologie（法国国家科学研究中心，天体粒子与宇宙学）；University of Białystok（比亚韦斯托克大学）；Institute for Quantum Studies, Chapman University（查普曼大学量子研究学院）
