Tightness of the imperfection-parameter dependence

Determine whether the gate lower bound for imperfectly prepared BB84 input states has tight dependence on the trace-distance imperfection parameter $\eta$.

Background

The paper extends its security analysis from ideal BB84 states to input states within trace distance η\eta of the ideal states. The resulting security region incorporates an η\eta-dependent degradation, but the authors do not establish that this dependence is optimal. Determining tightness would clarify whether the quantitative robustness guarantee reflects the actual limits of the protocol.

References

We have not shown that our bound is tight in terms of its behaviour with $\eta$.

— Quantum gate lower bounds for loss-tolerant position verification  (2608.16495 - May et al., 17 Aug 2026) in Section 6, “Discussion”