Belangrijkste concepten
There is quantum advantage in non-binary output non-interactive source simulation (NISS) scenarios, but not in binary output NISS scenarios.
Samenvatting
The paper considers two variations of the standard non-interactive source simulation (NISS) problem:
Entanglement-Assisted NISS (EA-NISS): In addition to the correlated classical sequences (Xd, Yd), the agents Alice and Bob have access to a shared Bell state. They perform measurements on their respective parts of the entangled state and use the classical outputs along with (Xd, Yd) to simulate a target distribution QU,V.
Classical Common Randomness NISS (CR-NISS): In addition to the correlated classical sequences (Xd, Yd), the agents have access to a shared classical common random bit Z. They use (Z, Xd) and (Z, Yd) to simulate QU,V.
The key findings are:
For binary-output NISS scenarios, the set of feasible distributions for EA-NISS and CR-NISS are equal. Hence, there is no quantum advantage in these scenarios.
For non-binary output NISS scenarios, the set of distributions that can be simulated in the CR-NISS scenario has measure zero within the set of distributions simulatable in the EA-NISS scenario. This demonstrates quantum advantage in non-binary output NISS.
The proofs rely on Fourier analysis techniques and show that any distribution generated in the EA-NISS scenario can be simulated in the corresponding CR-NISS scenario for the binary output case, while the converse is not true for the non-binary case.