  We analyze utility of communication channels in absence of any short of
quantum or classical correlation shared between the sender and the receiver. To
this aim, we propose a class of two-party communication games, and show that
the games cannot be won given a noiseless $1$-bit classical channel from the
sender to the receiver. Interestingly, the goal can be perfectly achieved if
the channel is assisted with classical shared randomness. This resembles an
advantage similar to the quantum superdense coding phenomenon where pre-shared
entanglement can enhance the communication utility of a perfect quantum
communication line. Quite surprisingly, we show that a qubit communication
without any assistance of classical shared randomness can achieve the goal, and
hence establishes a novel quantum advantage in the simplest communication
scenario. In pursuit of a deeper origin of this advantage, we show that an
advantageous quantum strategy must invoke quantum interference both at the
encoding step by the sender and at the decoding step by the receiver. We also
study communication utility of a class of non-classical toy systems described
by symmetric polygonal state spaces. We come up with communication tasks that
can be achieved neither with $1$-bit of classical communication nor by
communicating a polygon system, whereas $1$-qubit communication yields a
perfect strategy, establishing quantum advantage over them. To this end, we
show that the quantum advantages are robust against imperfect
encodings-decodings, making the protocols implementable with presently
available quantum technologies.
