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.