Abstract
Mathias Christandl (Lehrstuhl für theoretische Festkörperphysik, Munich, Germany)
Post-Selection Technique for Permutation-Invariant Quantum Channels
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.
Our method 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.
We note that our results can be generalised to quantum channels that
commute with the action of an arbitrary finite or compact group.