Tighter sequential conjugate-coding POVM bound

Determine whether the additive O(ε^{1/4}) term in the sequential conjugate-coding security bound of Theorem 3.1 can be improved to O(ε^{1/2}) or better by employing a more refined analysis.

Background

The central technical contribution is a sequential bound showing that any POVM which identifies computational-basis m-qubit states with success 1−ε yields at most 2^{-m}+O(ε^{1/4}) guessing probability for the corresponding Hadamard-basis string, even when the basis is revealed post-measurement. Improving the ε-exponent would strengthen the security and potentially reduce resource requirements by increasing the min-entropy in the conjugate basis.

In the conclusion, the authors explicitly flag the tightness of this bound as an open direction and ask whether a better dependence on ε can be proven, such as O(ε^{1/2}).