Fidelity Bounds for Device-Independent Advantage Distillation

TL;DR

This paper develops an algorithm to compute tight lower bounds on fidelity for device-independent advantage distillation, enhancing noise tolerance analysis and security proofs in quantum key distribution.

Contribution

It introduces an algorithm for arbitrarily tight fidelity bounds, improving security analysis and potentially aiding in keyrate calculations for device-independent QKD protocols.

Findings

Developed an algorithm for tight fidelity bounds

Provided new insights into security conditions

Conjectured a necessary security condition

Abstract

It is known that advantage distillation (that is, information reconciliation using two-way communication) improves noise tolerances for quantum key distribution (QKD) setups. Two-way communication is hence also of interest in the device-independent case, where noise tolerance bounds for one-way error correction are currently too low to be experimentally feasible. Existing security proofs for the device-independent repetition-code protocol (the most prominent form of advantage distillation) rely on fidelity-related security conditions, but previous bounds on the fidelity were not tight. We improve on those results by developing an algorithm that returns arbitrarily tight lower bounds on the fidelity. Our results give new insight on how strong the fidelity-related security conditions are, and could also be used to compute some lower bounds on one-way protocol keyrates. Finally, we conjecture a necessary security condition for the protocol studied in this work, that naturally complements the existing sufficient conditions.