On Random Purifications of Isometries and Channels

arXiv:2611.04573v1 Announce Type: new Abstract: Acorn tricks turn weak quantum resources into stronger "randomized" ones. A recent example is the random purification channel, which turns $t$ copies of a mixed state into $t$ copies of a random purification. We ask whether analogous techniques can turn queries to an isometry into queries to a random unitary completion, or queries to a quantum channel into queries to a random isometry dilation. For an isometry from dimension $N$ to dimension $M$, we give an efficient, stateful simulator for $T$ sequential, forward queries to a fixed Haar random unitary completion. It uses at most one forward isometry query per simulated call, with total trace-distance error $O(T\sqrt{N/(M-T)})$.