  We propose a general method for studying properties of quantum channels
acting on an n-partite system, whose action is invariant under permutations of
the subsystems. Our main result is that, in order to prove that a certain
property holds for any arbitrary input, it is sufficient to consider the
special case where the input is a particular de Finetti-type state, i.e., a
state which consists of n identical and independent copies of an (unknown)
state on a single subsystem. A similar statement holds for more general
channels which are covariant with respect to the action of an arbitrary finite
or locally compact group.
  Our technique can be applied to the analysis of information-theoretic
problems. For example, in quantum cryptography, we get a simple proof for the
fact that security of a discrete-variable quantum key distribution protocol
against collective attacks implies security of the protocol against the most
general attacks. The resulting security bounds are tighter than previously
known bounds obtained by proofs relying on the exponential de Finetti theorem
[Renner, Nature Physics 3,645(2007)].
