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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Abstract

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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Cited by

[1] Sahil Gopalkrishna Naik, Govind Lal Sidhardh, Samrat Sen, Arup Roy, Ashutosh Rai, and Manik Banik, "Distilling Nonlocality in Quantum Correlations", arXiv:2208.13976, (2022).

[2] Martin J. Renner, Armin Tavakoli, and Marco Túlio Quintino, "Classical Cost of Transmitting a Qubit", Physical Review Letters 130 12, 120801 (2023).

[3] Mayalakshmi K, Thigazholi Muruganandan, Sahil Gopalkrishna Naik, Tamal Guha, Manik Banik, and Sutapa Saha, "Bipartite polygon models: entanglement classes and their nonlocal behaviour", arXiv:2205.05415, (2022).

[4] Péter Diviánszky, István Márton, Erika Bene, and Tamás Vértesi, "Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant", Scientific Reports 13, 13200 (2023).

[5] Ananya Chakraborty, Sahil Gopalkrishna Naik, Edwin Peter Lobo, Ram Krishna Patra, Samrat Sen, Mir Alimuddin, Amit Mukherjee, and Manik Banik, "Advantage of Qubit Communication Over The C-bit in Multiple Access Channel", arXiv:2309.17263, (2023).

[6] Teiko Heinosaari, Oskari Kerppo, Leevi Leppäjärvi, and Martin Plávala, "Simple information-processing tasks with unbounded quantum advantage", Physical Review A 109 3, 032627 (2024).

[7] Mir Alimuddin, Ananya Chakraborty, Govind Lal Sidhardh, Ram Krishna Patra, Samrat Sen, Snehasish Roy Chowdhury, Sahil Gopalkrishna Naik, and Manik Banik, "Advantage of Hardy's nonlocal correlation in reverse zero-error channel coding", Physical Review A 108 5, 052430 (2023).

[8] Jef Pauwels, Stefano Pironio, Emmanuel Zambrini Cruzeiro, and Armin Tavakoli, "Adaptive Advantage in Entanglement-Assisted Communications", Physical Review Letters 129 12, 120504 (2022).

[9] Sahil Gopalkrishna Naik, Edwin Peter Lobo, Samrat Sen, Ram Krishna Patra, Mir Alimuddin, Tamal Guha, Some Sankar Bhattacharya, and Manik Banik, "Composition of Multipartite Quantum Systems: Perspective from Timelike Paradigm", Physical Review Letters 128 14, 140401 (2022).

[10] Zhonghua Ma, Markus Rambach, Kaumudibikash Goswami, Some Sankar Bhattacharya, Manik Banik, and Jacquiline Romero, "Randomness-Free Test of Nonclassicality: A Proof of Concept", Physical Review Letters 131 13, 130201 (2023).

[11] Carlos Vieira, Carlos de Gois, Lucas Pollyceno, and Rafael Rabelo, "Interplays between classical and quantum entanglement-assisted communication scenarios", New Journal of Physics 25 11, 113004 (2023).

[12] Subhendu B. Ghosh, Snehasish Roy Chowdhury, Tathagata Gupta, Anandamay Das Bhowmik, Sutapa Saha, Some Sankar Bhattacharya, and Tamal Guha, "Local Inaccessibility of Random Classical Information : Conditional Nonlocality demands Entanglement", arXiv:2307.08457, (2023).

[13] Sahil Gopalkrishna Naik, Edwin Peter Lobo, Samrat Sen, Ramkrishna Patra, Mir Alimuddin, Tamal Guha, Some Sankar Bhattacharya, and Manik Banik, "Composition of multipartite quantum systems: perspective from time-like paradigm", arXiv:2107.08675, (2021).

[14] Chen Ding, Edwin Peter Lobo, Mir Alimuddin, Xiao-Yue Xu, Shuo Zhang, Manik Banik, Wan-Su Bao, and He-Liang Huang, "Quantum Advantage: A Single Qubit's Experimental Edge in Classical Data Storage", arXiv:2403.02659, (2024).

The above citations are from SAO/NASA ADS (last updated successfully 2024-05-26 09:11:49). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2024-05-26 09:11:47).