Abstract
We introduce the task of shadow process simulation, where the goal is to simulate the estimation of the expectation values of arbitrary quantum observables at the output of a target physical process. When the sender and receiver share random bits or other no-signaling resources, we show that the performance of shadow process simulation exceeds that of conventional process simulation protocols in a variety of scenarios including communication, noise simulation, and data compression. Remarkably, we find that there exist scenarios where shadow simulation provides increased statistical accuracy without any increase in the number of required samples.