Postselection technique for optical Quantum Key Distribution with improved de Finetti reductions

TL;DR

This paper rigorously refines the postselection technique for optical quantum key distribution, extending its applicability and improving de Finetti reductions, leading to better security proofs against coherent attacks.

Contribution

The authors provide a rigorous mathematical foundation for postselection, extend its use to prepare-and-measure and decoy-state protocols, and develop a new variant of the flag-state squasher.

Findings

Postselection technique outperforms other proof methods against coherent attacks.

Improved de Finetti reductions reduce impact on key rate.

Application to time-bin encoded three-state protocol demonstrates effectiveness.

Abstract

The postselection technique is an important proof technique for proving the security of quantum key distribution protocols against coherent attacks. In this work, we go through multiple steps to rigorously apply the postselection technique to optical quantum key distribution protocols. First, we place the postselection technique on a rigorous mathematical foundation by fixing a technical flaw in the original postselection paper. Second, we extend the applicability of the postselection technique to prepare-and-measure protocols by using a de Finetti reduction with a fixed marginal. Third, we show how the postselection technique can be used for decoy-state protocols by tagging the source. Finally, we extend the applicability of the postselection technique to realistic optical setups by developing a new variant of the flag-state squasher. We also improve existing de Finetti reductions, which reduce the effect of using the postselection technique on the key rate. These improvements can be more generally applied to other quantum information processing tasks. As an example to demonstrate the applicability of our work, we apply our results to the time-bin encoded three-state protocol. We observe that the postselection technique performs better than all other known proof techniques against coherent attacks.