Abstract
complete description of quantum information theory needs to incorporate simultaneously at least three important concepts or principles, namely: (a) quantum entanglement, (b) quantumcoherence versus decoherence (i.e., in the presence of dissipation),and (c) the quantum- classical limit (or quantum-classical interface). We discuss how the concept of quantum phasespace can be enlarged to provide just such a unified and consistent description. Quantum phase-space methods and, especially, such quantum phase-space distribution functionsas the P-, Q-, Wigner and Weyl functions, have played an important role over many years in quantum mechanics and such allied areas as quantum optics. We introduce here in a very fundamental manner a natural hierarchy of extended quantum phase spaces and associated extended distribution functions with the capacity to describe simultaneously both quantum noise and quantum correlations at increasingly higher-order levels. We show further how the extendedphase-space formalism provides valuable insights into the important issue of quantum versus classical correspondence, and also how it has extremely appealing properties for a consistent description of quantum information theory. At the next-to-lowest (x-p-X-P) level in the extendedhierarchy the description of mixed states becomes unified, and a very convenient means is opened up, for example, to discuss together, and on the same footing, the ordinary Wigner and Weyl functions of a quantal system. The doubling of the number of degrees of freedom, which, rather surprisingly, has its roots in classical mechanics, has strong overlaps with a similar feature of thermo-field dynamics, and hence with the treatment of quantum systems subject to thermal noise.
