Localized states (qubits), entanglement and decoherence from Wigner zoo

摘要

We present the application of the variational-wavelet analysis to the calculations and analysis of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems [1, 2], (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points. We construct the solutions via the multiscale expansions in the high-localized nonlinear eigenmodes in the base of the compactly supported wavelets and the wavelet packets. We demonstrate the appearance of (stable) localized patterns (waveletons) and consider entanglement and decoherence as possible applications. Our goals are some attempt of classification and the explicit numerical-analytical constructions of the existing zoo of possible/realizable quantum states. There is a hope on the understanding of relation between the structure of initial Hamiltonians and the possible types of quantum states and the qualitative type of their behaviour. Inside the full spectrum there are at least f(impossibilities which are the most important from our point of view for possible realization of quantum-like computations: localized states, chaotic-like or/and entangled patterns, localized (stable) patterns (waveletons).