# Phonon Decoherance

Quantum computational and communication ideas rely on the fundamental physical notions of superposition, entanglement, and interference and thus on a coherent evolution.

Decoherence, which destroys the unitary evolution of the coherent state is the major show-stopper of an effective practical realization of the above ideas. The system interacts with the environment so that system and environment states entangle into a common, usually macroscopic state. The system state is obtained after a trace on the additional variables, which rules out certain correlations. The theory of decoherence addresses the manner in which some quantum systems become classical due to such entanglement with the environment. The latter in effect monitors certain observables in the system, destroying coherence between the states corresponding to their eigenvalues. Only preferred survive consecutive 'measurements' by the environment. The rest of the states, which actually comprise a major part of the Hilbert space are eliminated. Many of the features of 'classical' systems are actually induced in quantum systems by their environment.

The Phonon Decoherence (PD) tool provides tools for analysis of the evolution of an initially entangled electron state which evolves in presence of semiconductor lattice vibrations - phonons. The initial electron state is constructed by a superposition of two Gaussian wave packets and has a pronounced interference term comprised of alternating positive and negative values of the Wigner function. The simulations show how the phonons effectively destroy the interference term. The initial coherence in wave vector distribution is pushed towards the equilibrium distribution. Phonons hinder the natural spread of the density with time pushing towards a classical localization. The initially pure electron state evolves towards a state with an entirely different physical interpretation: it is a mixed state where the electron can be with given probability in one of the two Gaussian packets. The decoherence effect of the phonons causing transition from quantum to classical state is demonstrated by the purity of the state, which decreases from itâ€™s initial value of 1, with a speed depending on the lattice temperature.