  In this paper we are discussing the question how a continuous quantum system
can be simulated by mean field fluctuations of a finite number of qubits. On
the kinematical side this leads to a convergence result which states that
appropriately chosen fluctuation operators converge in a certain weak sense
(i.e. we are comparing expectation values) to canonical position and momentum
Q, P of one-degree of freedom, continuous quantum system. This result is
substantially stronger than existing methods which rely either on central limit
theorem arguments (and are therefore restricted to the Gaussian world) or are
valid only if the states of the ensembles are close to the "fully polarized"
state. Dynamically this relationship keeps perfectly intact (at least for small
times) as long as the continuous system evolves according to a quadratic
Hamiltonian. In other words we can approximate the corresponding (Heisenberg
picture) time evolution of the canonical operators Q, P up to arbitrary
accuracy by the appropriately chosen time evolution of fluctuation operators of
the finite systems.
