You can feel an unfamiliar object along its length, across its width, or diagonally: each time gaining new information. But what if one way of feeling tells you absolutely nothing about what another would reveal? That's exactly how mutually unbiased bases work in quantum mechanics: measuring in one of them leaves you completely in the dark about the outcome in another.

The authors of the new work found an elegant recipe for preparing such sets. They enlisted "bent functions"—mathematical objects that behave as unpredictably as possible, like a cipher where each symbol is independent of the rest. With their help, they managed to write out the new basis vectors directly as combinations of ordinary ones, as if a complex pattern were suddenly unraveled into simple stitches.

The practical payoff of this mathematical beauty is enormous. When physicists reconstruct an unknown quantum state from a series of measurements, they need exactly such sets: they allow a complete picture to be assembled in a minimal number of steps. The new construction not only works but also makes the process more transparent: every step can be followed like a musical score. And it all started with simple feeling — only now we know how to make it truly independent.