Classical analogue of quantum superdense coding and communication advantage of a single quantum system

Ram Krishna Patra1, Sahil Gopalkrishna Naik1, Edwin Peter Lobo2, Samrat Sen1, Tamal Guha3, Some Sankar Bhattacharya4, Mir Alimuddin1, and Manik Banik1

1Department of Physics of Complex Systems, S.N. Bose National Center for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India.
2Laboratoire d’Information Quantique, Université libre de Bruxelles (ULB), Av. F. D. Roosevelt 50, 1050 Bruxelles, Belgium
3Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong.
4International Centre for Theory of Quantum Technologies, University of Gdansk, Wita Stwosza 63, 80-308 Gdansk, Poland.

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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.

In various daily-life experiences, the direct cause-effect relation between two events can be amplified through a third event influencing both of the other two events. Similarly, within the domain of information transmission, quantum superdense coding stands as a pioneering example wherein a shared quantum correlation, devoid of any communicative power, augments classical communication efficacy of a quantum channel. The present study illustrates a parallel occurrence involving classical correlation and a classical communication channel. Specifically, it presents an example of a communication task that remains elusive with one bit of classical communication only, but can be done perfectly when the bit channel is assisted with classical correlation. Intriguingly, optimal task performance is achieved through the transmission of a two-level quantum system, unaided by any shared correlation. These findings, on one hand, establish a novel quantum advantage and, on the other hand, underscore the need to reassess the presumption of cost-free classical correlation sharing in various classical communication tasks.

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