On the Optimality of a Quantum Key Distribution

TL;DR

This paper introduces a method to evaluate whether a quantum key distribution protocol operates optimally by defining a measure called optimality, applicable in asymptotic scenarios, and discusses how to achieve this optimality.

Contribution

It proposes a formal definition of optimality for QKD protocols and introduces optimal versions of BB84 and twin-field QKD, along with methods to attain maximum efficiency.

Findings

Defined a measure called optimality for QKD systems.

Presented optimal versions of BB84 and twin-field QKD.

Outlined conditions for achieving maximum efficiency in QKD.

Abstract

Quantum key distribution (QKD) systems require optimal performance of both quantum and classical channels - utilizing as few as possible qubits and bits for establishing as many as possible key bits. Here we report a way to determine if a quantum key distribution model (or protocol) operates in an optimal behavior. This is accomplished by introducing a quantity, called optimality, which is the maximum over the total efficiency of a QKD under any circumstances (any values of QKD parameters). The optimality definition is given for the asymptotic operation of a QKD system - when infinitely many quantum systems are transferred/used in a quantum key distribution protocol or a quantum key distribution system is used infinitely many times. A way to attain the optimality is considered\textemdash implementation of a completely efficient QKD system (a combination of capacity-reaching quantum channel and a completely compressed classical channel) is presented. Optimal versions of BB84-QKD and twin-field QKD are introduced.