Post-selection technique for quantum channels with applications to
quantum cryptography
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)]. This is joint work with
Robert Koenig and Renato Renner http://arxiv.org/abs/0809.3019