  The de Finetti representation theorem for continuous variable quantum system
is first developed to approximate an N-partite continuous variable quantum
state with a convex combination of independent and identical subsystems, which
requires the original state to obey permutation symmetry conditioned on
successful experimental verification on k of N subsystems. We generalize the de
Finetti theorem to include asymmetric bounds on the variance of canonical
observables and biased basis selection during the verification step. Our result
thereby enables application of infinite-dimensional de Finetti theorem to
situations where two conjugate measurements obey different statistics, such as
the security analysis of quantum key distribution protocols based on squeezed
state against coherent attack.
