Generalized State Discrimination for Tunable Quantum Key Distribution: The phiQKD Protocol

We introduce a tunable framework for generalized quantum state discrimination (GSD) and apply it to quantum key distribution (QKD) through a protocol we call phiQKD. Building upon the two-state B92 protocol, phiQKD replaces the traditional unambiguous state discrimination (IDP) measurement with a one-parameter family of hybrid POVMs characterized by a tilting angle $\phi$. This allows for continuous control over the trade-off among correct, incorrect, and inconclusive outcomes. While the asymptotic key rate improvement over B92 is modest, phiQKD offers a practical advantage by enabling adaptability to noise and channel imperfections via measurement tunability. By evaluating the protocol under asymptotic, finite-key, and composable security models, we show that, treating quantum measurement as a tunable design parameter, rather than a fixed operation, enables flexible protocol optimization and improved performance under realistic constraints.