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arXiv:2504.11315 · IEEE International Conference on Quantum Computing and Engineering (QCE)

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

Trevor N. Thomas, Walter O. Krawec

Published Aug 30, 2025• 2 citations
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Abstract

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.

DOI
10.1109/qce65121.2025.00104

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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.
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High-dimensional states (HD) are promising for quantum key distribution (QKD) due to their noise tolerance and efficiency. However, creating, and measuring, HD states is technologically challenging, thus making it important to study HD-QKD protocols where Alice and Bob are restricted in their quantum capabilities. In this paper, we revisit an HD-QKD protocol, introduced in (PRA 97 (4):042347), which does not require Alice and Bob to be capable of sending and measuring in full mutually unbiased bases. The previous proof of security for this protocol has relied on numerical methods. In this work, we provide a new proof of security, enabling the key-rate evaluation beyond previous work. Furthermore, our new proof produces better results for certain channel and dimension scenarios than prior work.
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The application of quantum mechanics contributes to the field of cryptography with very important advantage as it offers a mechanism for detecting the eavesdropper. The pioneering work of quantum key distribution uses mutually unbiased bases (MUBs) to prepare and measure qubits (or qudits). Weak mutually unbiased bases (WMUBs) have weaker properties than MUBs properties, however, unlike MUBs, a complete set of WMUBs can be constructed for systems with composite dimensions. In this paper, we study the use of weak mutually unbiased bases (WMUBs) in quantum key distribution for composite dimensional finite systems. We prove that the security analysis of using a complete set of WMUBs to prepare and measure the quantum states in the generalized BB84 protocol, gives better results than using the maximum number of MUBs that can be constructed, when they are analyzed against the intercept and resend attack.