Three-intensity decoy state method for device independent quantum key distribution with basis dependent errors

TL;DR

This paper develops a practical three-intensity decoy-state method for device-independent quantum key distribution, addressing basis-dependent errors and demonstrating that high source coding precision is unnecessary for security.

Contribution

It introduces general formulas for a three-state decoy method applicable to imperfect sources and shows that less precise source coding still guarantees security in MDIQKD.

Findings

Decoy-state formulas applicable to three states and imperfect sources.

Secure QKD can tolerate less precise source coding than previously thought.

Loosening source coding accuracy does not compromise security.

Abstract

We study the measurement device independent quantum key distribution (MDIQKD) in practice with limited resource, when there are only 3 different states in implementing the decoy-state method and when there are basis dependent coding errors. We present general formulas for the decoy-state method for two-pulse sources with 3 different states, which can be applied to the recently proposed MDIQKD with imperfect single-photon source such as the coherent states or the heralded states from the parametric down conversion. We point out that the existing result for secure QKD with source coding errors does not always hold. We find that very accurate source coding is not necessary. In particular, we loosen the precision of existing result by several magnitude orders for secure QKD.