Deterministic generation of Gaussian pure states in a quasilocal dissipative system

This paper shows that an arbitrary Gaussian pure state can be deterministically generated in a dissipative open system that has quasilocal interactions between the subsystems and couples to the surrounding environment in a local manner. A quasilocal interaction, which means that the interaction occurs among only a few subsystems, is a crucial requirement for practical engineering of a dissipative system. The key idea is that first an auxiliary system having a local interaction with the environment is prepared and then that auxiliary system is coupled to the underlying target system via a set of two-body Hamiltonians in such a way that a desired pure state is generated. Moreover, we show that even with a simple single-mode auxiliary system, the deterministic generation of an arbitrary approximate Gaussian cluster state is possible by devising an appropriate switching scheme. We discuss in a specific example how much a dissipation-induced pure Gaussian state can be perturbed by decoherence and parameter error.