Pseudorandom unitaries can be built without statistical randomness.

Quantum computers rely on operations called unitaries. Researchers often study quantum pseudorandomness, which means operations that look completely random even when they follow strict rules. This comes in two flavors: statistical randomness, like unitary designs, and computational randomness, which fools computers. Scientists used to think building computational pseudorandom unitaries required statistical randomness as a starting ingredient. The researchers wanted to see if that requirement was true. They proved that statistical pseudorandomness is not necessary. Instead of using statistically random layers, they used quantum ensembles that are not even state 1-designs. The key was ensuring the operations are sufficiently distinct, meaning they separate states well enough. This distinct property is actually necessary for any pseudorandom unitary. Their method successfully created new non-adaptively secure pseudorandom unitaries without any statistical randomness. They also showed how this distinctness rule limits properties like quantum coherence and imaginary numbers.

Why it matters

This clarifies the foundations of quantum randomness, which is crucial for developing secure quantum technologies. It shows computational security in quantum systems can be achieved without relying on statistical randomness, potentially simplifying designs.

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