New Key Rate Bound for High-Dimensional BB84 with Multiple Basis Measurements

In this paper we derive a new bound on the secret key-rate of the High Dimensional BB84 protocol operating with multiple mutually unbiased bases (MUBs). To our knowledge, our proof is the first for this protocol that is both general (in that it can handle arbitrary, asymmetric channels), and also the first that derives a bound on the quantum min entropy for general attacks, without relying on post selection techniques or the asymptotic equipartition property. Because of this, our new result shows that far more optimistic key-rates are possible for a low number of signals, even in general channels. Furthermore, our proof methods may be broadly applicable to other protocols relying on multiple measurement bases and we prove several technical lemmas that may have independent interest. We evaluate our new bound and compare to prior work, showing that higher key-rates are possible in several operating scenarios. We also show some interesting behavior of the protocol when faced with asymmetric noise.