Refined promise-aware measures ruling out speedups

Develop more fine-grained variants of promise-aware complexity measures (such as promised block sensitivity and promised certificate complexity) that can be used to prove the non-existence of superpolynomial quantum speedups for broader classes of partial Boolean functions.

Background

The paper introduces and relates several promise-aware measures for partial functions, yielding conditions under which deterministic and quantum complexities are polynomially related.

Further refinements of these measures might strengthen the non-speedup criteria and extend them to additional domains and function classes.

References

We list some open problems that would further the usefulness of our techniques. Are there more fine-grained versions of the promise measures discussed in~\Cref{sec:promise_measures} which allow us to show the non-existence of a superpolynomial speedup?

— From Promises to Totality: A Framework for Ruling Out Quantum Speedups  (2603.29256 - Huffstutler et al., 31 Mar 2026) in Discussion and further work (Introduction)