seminar: Extended Quantum Phase-Space Formulations of Many-Body Theory and Quantum Information Theory
speaker: Raymond Bishop (School of Physics and Astronomy, The University of Manchester)abstract: A complete description of quantum information theory needs to take into account simultaneously at least three important concepts or principles, namely: (a) quantum entanglement, (b) quantum coherence 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 phase space can be enlarged to provide just such a unified and consistent description. The usual (x-p} phase-space formulation of quantum mechanics has its practical origins in work of Wigner from over 70 years ago, where he originated the idea of a quantum phase-space distribution function. The formalism has since been developed and utilised in many fields of physics, including statistical physics, quantum optics and electronics, collision theory, and quantum chaos. It has the especially attractive feature that it provides a framework in which quantal phenomena can be described using as much classical language as possible. The phase-space formalism provides important insights into one of the key issues, namely of quantum-classical correspondence or non-correspondence. Here we show how, by going right back to a reformulation of classical mechanics in an extended (x-p-X-P} phase space, one can also introduce a corresponding extended quantum phase space with extremely appealing properties for a consistent description of quantum information theory. 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. We show how the extended (x-p-X-P} phase space also provides a natural means to describe simultaneously the quantum fluctuations or quantum noise (in the {x-p} variables) and the quantum correlations (in the {X-P} variables present in a quantal system. Thus, the extended quantum phase-space framework provides a very natural vehicle to discuss all three of the above-mentioned concepts inherent to quantum information theory. It also unifies the description of mixed states, and provides a means to discuss together the Wigner and Weyl functions of a quantal system. Finally, the framework enables us to utilise in a very unified fashion the coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at finite temperature, that we have introduced previously as a "random" (or "thermal" or "noisy") basis in Hilbert space.
timetable:
Thu 29 Mar, 14:30 - 15:00, Aula Dini
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