Key Rate Analysis of a 3-State Twin-Field Quantum Key Distribution Protocol in the Finite-key Regime

When analysing Quantum Key Distribution (QKD) protocols several metrics can be determined, but one of the most important is the Secret Key Rate. The Secret Key Rate is the number of bits per transmission that result in being part of a Secret Key between two parties. There are equations that give the Secret Key Rate, for example, for the BB84 protocol, equation 52 from [1, p.1032] gives the Secret Key Rate for a given Quantum Bit Error Rate (QBER). However, the analysis leading to equations such as these often rely on an Asymptotic approach, where it is assumed that an infinite number of transmissions are sent between the two communicating parties (henceforth denoted as Alice and Bob). In a practical implementation this is obviously impossible. Moreover, some QKD protocols belong to a category called Asymmetric protocols, for which it is significantly more difficult to perform such an analysis. As such, there is currently a lot of investigation into a different approach called the Finite-key regime. Work by Bunandar et al. [2] has produced code that used Semi-Definite Programming to produce lower bounds on the Secret Key Rate of even Asymmetric protocols. Our work looks at devising a novel QKD protocol taking inspiration from both the 3-state version of BB84 [3], and the Twin-Field protocol [4], and then using this code to perform analysis of the new protocol.