Quantum statistical effect induced through conditioned post-processing procedures with unitary $t$-designs

We propose a few-body quantum phenomenon, which manifests itself through stochastic state preparations and measurements followed by a conditioned post-processing procedure. We show two experimental protocols to implement these phenomena with existing quantum computers, and examine their feasibility by using simulations. Our simulation results suggest that the experimental demonstration is feasible if we repeat the state preparations and measurements about thirty thousand times to three-qubit systems.