Zoom 회의 ID: 356 501 3138 / 암호: 471247
We develop a theory of Gaussian states and channels over general quantum kinematical systems with finitely many degrees of freedom. The underlying phase space is described by a locally compact abelian group G with a symplectic structure determined by a 2-cocycle on G. We completely characterize Gaussian states over groups of the form G=F×F^ when F is either totally disconnected and 2-regular, or the torus T. As a corollary, we generalize the discrete Hudson theorem to finite 2-regular groups. We introduce the class of metaplectic quantum channels, a generalization of linear bosonic channels, and obtain Gaussian channels as natural subclasses. We exhibit single letter formulae for the quantum capacity and regularized minimum output entropy for arbitrary Gaussian channels over finite 2-regular groups. In angle-number systems, we derive explicit formulae for the action of every Gaussian channel on the canonical matrix units.