Perfect discrimination of no-signalling channels via quantum superposition of causal structures

A no-signalling channel transforming quantum systems in Alice's and Bob's local laboratories is compatible with two different causal structures: (A⪯B) Alice's output causally precedes Bob's input and (B⪯A) Bob's output causally precedes Alice's input. Here I prove that two no-signalling channels that are not perfectly distinguishable in any ordinary quantum circuit can become perfectly distinguishable through the quantum superposition of circuits with different causal structures.