The world of quantum noise and the fundamental output process
A stationary theory of quantum stochastic processes of second order is outlined. It includes KMS processes in wide sense like the equilibrium finite temperature quantum noise given by the Planck's spectral formula. It is shown that for each stationary noise there exists a natural output process output process which is identical to the noise in the infinite temperature limit, and flipping with the noise if the time is reversed at finite temperature. A canonical Hilbert space representation of the quantum noise and the fundamental output process is established and a decomposition of their spectra is found. A brief explanation of quantum stochastic integration with respect to the input-output processes is given using only correlation functions. This provides a mathematical foundation for linear stationary filtering transformations of quantum stochastic processes. It is proved that the colored quantum stationary noise and its time-reversed version can be obtained in the second order theory by a linear nonadapted filtering of the standard vacuum noise uniquely defined by the canonical creation and annihilation operators on the spectrum of the input-output pair.