Source-linked AI summary
Post-selection technique for quantum channels with applications to quantum cryptography
Matthias Christandl, Robert Koenig, Renato Renner
TL;DR
The paper asks whether properties of permutation-invariant quantum channels can be verified without checking every possible input. It introduces a post-selection method using de Finetti states, yielding a simple route from QKD security against collective attacks to security against general attacks, with tighter bounds than exponential de Finetti proofs.
Problem
The paper addresses how to establish properties of permutation-invariant quantum channels for arbitrary inputs while enabling tractable analysis of information-theoretic protocols.
Method
The paper bounds the diamond-norm distance between symmetric maps by evaluating them on a purification of a particular de Finetti state, using permutation symmetry and symmetric-subspace reductions.
Results
For QKD, security against collective attacks implies security against general attacks, with tighter bounds than earlier exponential de Finetti-based proofs.
Takeaways & Limitations
The method provides a simple security proof for QKD and extends from permutation symmetry to covariance under arbitrary finite or locally compact groups.
Abstract
from arXiv · showhide
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)].