Statistical Dynamics of Coherent Quantum Systems Operating in the Presence of Quantum Noise

Abstract

A statistical characterization of the quantum state of polarization for a coherent quantum system disturbed by quantum noise is presented. The composite quantum system consists of an integer number N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> of mutually polarized photons disturbed by quantum noise which consists of an average number N of thermal radiation quanta plus the zero-point energy fluctuations. The interacting and coupled dynamics of the quantum system polarization is modeled by mutually coupled energy balanced stochastic differential equations mimicking the motion of Huygens mutually coupled pendulum clocks. The Markovian nature of the quantum noise allows one to use the Fokker-Planck (FP) apparatus to develop a coherency distribution which lives on a Clifford horn torus. Using this distribution, distributions for the Quantum State-of-Polarization, the Quantum Degree-of-Polarization, the circular moments, and the azimuthal and longitudinal polarization state jitters are derived. It is shown that the stable polarization states of quantum system equilibrium define a Bravais lattice in phase space. From this perspective, it is shown that quantum polarization interruptions are at the heart of certain quantum decoherence effects, e.g., polarization slips and flips, while pendula-like clock synchronization is at the heart of maintaining and sustaining coherency among the parts (photons) of coherent quantum systems. A classical world to quantum world “transition boundary” is identified as a function of quantum system parameters. This function is used to partition the electromagnetic spectrum into three disjoint regions of operation: a classical, a transition, and a quantum communications region. The results presented will find applications to the problem of evaluating single and multiphoton quantum communication system performance and in the system engineering design of quantum communication systems and a quantum internet connecting quantum computers.