Non-Gaussian Quantum States and Where to Find Them

Gaussian states have played an important role in the physics of continuous-variable quantum systems. They are appealing for experimental ease with which they can be produced, and their compact elegant mathematical description. Nevertheless, many proposed technologies require us to go beyond realm introduce non-Gaussian elements. In this Tutorial, we provide a roadmap states. We phase-space representations as framework describe different properties then use various ways explore structure state space. explain how characterized not only through negative values Wigner function, but also via other such non-Gaussianity related stellar rank. For multimode systems, naturally confronted question behave respect correlations. To answer question, first show created by performing measurements on subset modes state. Then, highlight that these measured must correlated specific correlations remainder system create or Wigner-negative On hand, operations shown enhance even Finally, demonstrate negativity is requirement violate Bell inequalities achieve computational advantage. At end overview several realizations optics beyond.Received 2 May 2021DOI:https://doi.org/10.1103/PRXQuantum.2.030204Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasMeasurement-based computingNonlocalityOptical information processingQuantum informationQuantum entanglementQuantum architectures & platformsQuantum processing continuous variablesQuantum opticsQuantum engineeringQuantum lightTechniquesPhase space methodsAtomic, Molecular OpticalQuantum Information