A pseudorandom unitary family is an efficiently implementable, secret-key indexed family of unitary operators that cannot be distinguished from a Haar-random unitary by the specified class of efficient quantum tests, except with negligible advantage. The allowed queries must be specified, including whether they may be adaptive or use the inverse operator. Computational indistinguishability is weaker than closeness of the underlying probability distributions.
Raza et al. (2026) showed that nonadaptively secure constructions can replace a statistically randomizing unitary-design layer by an ensemble satisfying a weaker distinctness property. Their depth-1 construction supplies this ingredient; it does not assert that a layer of independent single-qubit operations alone is a pseudorandom unitary family. The cryptographic components of the full construction remain necessary.
The distinctness argument was discovered with GPT-5.6 Sol and developed and checked by the authors. Independent external verification had not been reported as of Sep. 7, 2026.
