  Classical communication capacity of a channel can be enhanced either through
a device called a 'quantum switch' or by putting the channel in a quantum
superposition. The gains in the two cases, although different, have their
origin in the use of a quantum resource, but is it the same resource? Here this
question is explored through simulating large sets of random channels. We find
that quantum superposition always provides an advantage, while the quantum
switch does not: it can either increase or decrease communication capacity. The
origin of this discrepancy can be attributed to a subtle combination of
superposition and non-commutativity.
