Applications of Scrooge randomness

Determine whether Scrooge randomness generated naturally by deep thermalization and Hilbert-space ergodicity enables applications in quantum information science that cannot be achieved with Haar-randomness.

Background

Haar randomness is already useful for benchmarking, state learning, certification, and related quantum-information protocols, whereas Scrooge ensembles arise naturally under constraints such as finite temperature or conserved quantities. Because Scrooge randomness is more difficult to implement on digital hardware, its practical value remains less established.

The authors identify as unresolved whether the distinctive information-minimizing structure of Scrooge ensembles can provide capabilities beyond those available from Haar-random ensembles.