  According to the quantum de Finetti theorem, if the state of an N-partite
system is invariant under permutations of the subsystems then it can be
approximated by a state where almost all subsystems are identical copies of
each other, provided N is sufficiently large compared to the dimension of the
subsystems. The de Finetti theorem has various applications in physics and
information theory, where it is for instance used to prove the security of
quantum cryptographic schemes. Here, we extend de Finetti's theorem, showing
that the approximation also holds for infinite dimensional systems, as long as
the state satisfies certain experimentally verifiable conditions. This is
relevant for applications such as quantum key distribution (QKD), where it is
often hard - or even impossible - to bound the dimension of the information
carriers (which may be corrupted by an adversary). In particular, our result
can be applied to prove the security of QKD based on weak coherent states or
Gaussian states against general attacks.
