Real-Valued Somewhat-Pseudorandom Unitaries

arXiv:2403.16704v1 Announce Type: cross
Abstract: We explore a very simple distribution of unitaries: random (binary) phase -- Hadamard -- random (binary) phase -- random computational-basis permutation. We show that this distribution is statistically indistinguishable from random Haar unitaries for any polynomial set of orthogonal input states (in any basis) with polynomial multiplicity. This shows that even though real-valued unitaries cannot be completely pseudorandom (Haug, Bharti, Koh, arXiv:2306.11677), we can still obtain some pseudorandom properties without giving up on the simplicity …

arxiv binary computational cs.cr distribution input quant-ph random real simple states