We prove that continuous variable quantum information processing via Gaussian preserving operations, with Gaussian input states plus a (highly nonclassical) Fock number state, and subject to homodyne measurements and feedforward, can be efficiently simulated on a classical computer. This result reinforces the importance of the cubic phase state as an offline resource for universal continuous variable quantum information processing. We study the practical realization of this state by determining the Wigner function for an approximate cubic phase state prepared via two-mode squeezing with postselection on the signal field by displacing and counting photons in the idler field.
We study the quantum to classical transition in bipartite entangled systems in which one system is continuously coupled to a measurement apparatus as in the von Neumann model of quantum measurement. As an example, we study the open system dynamics of a particle in a harmonic well whose motion in the well is coupled to the internal spin. This system provides a rich illustration of the quantum to classical transition in weakly measured coupled systems. We analyze and derive conditions for which the dual constraints of strong localization/small noise required for the quantum-classical transition are satisfied for both regular and chaotic dynamics. We also study the dynamics of bipartite entanglement in the regime where classical trajectories emerge in the measurement record. Our analysis shows the surprising result that bipartite entanglement can persist in the classical limit.