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.