Post-selection technique for quantum channels with applications to quantum cryptography

TL;DR

This paper introduces a permutation-invariant method for analyzing quantum channels, simplifying security proofs in quantum cryptography by reducing complex scenarios to a special de Finetti-type state, leading to tighter security bounds.

Contribution

It presents a general technique for studying permutation-invariant quantum channels, enabling simplified security proofs in quantum cryptography with improved bounds.

Findings

Security against collective attacks implies security against general attacks.

Tighter security bounds than previous methods.

Applicable to channels covariant under group actions.

Abstract

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)].