No abstract

We analyze the communication utility of a single quantum system when the sender and receiver share neither any entanglement nor any classical shared randomness. To this aim, we propose a class of two-party communication games that cannot be won with a noiseless 1-bit classical channel, whereas the goal can be perfectly achieved if the channel is assisted by classical shared randomness. This resembles an advantage similar to the quantum superdense coding phenomenon where preshared entanglement can enhance 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. A subclass of these games can be won deterministically if the sender communicates some non-classical toy systems described by symmetric polygonal state spaces. We then proceed to design a variant of the game that can be won neither with 1-bit communication nor with a polygon system, but 1-qubit communication yields a perfect strategy, establishing a strict quantum nature of the advantage. To this end, we show that the quantum advantages are robust against imperfect encodings-decodings, making the protocols implementable with presently available quantum technologies.