Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a resource called shared randomness, quantum systems provide an advantage over their classical counterpart. Precisely, we show that appropriate albeit fixed measurements on a shared two-qubit state can generate correlations which cannot be obtained from any possible state on two classical bits. In a resource theoretic set-up, this feature of quantum systems can be interpreted as an advantage in winning a two players co-operative game, which we call the `non-monopolize social subsidy' game. It turns out that the quantum states leading to the desired advantage must possess non-classicality in the form of quantum discord. On the other hand, while distributing such sources of shared randomness between two parties via noisy channels, quantum channels with zero capacity as well as with classical capacity strictly less than unity perform more efficiently than the perfect classical channel. Protocols presented here are noise-robust and hence should be realizable with state-of-the-art quantum devices.
 L. Jiang, J. M. Taylor, N. Khaneja, and M. D. Lukin, ``Optimal approach to quantum communication using dynamic programming,'' Proceedings of the National Academy of Sciences 104, 17291–17296 (2007).
 A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, ``Gigahertz decoy quantum key distribution with 1 mbit/s secure key rate,'' Optics Express 16, 18790 (2008).
 S. Wengerowsky, et. al. ``Entanglement distribution over a 96-km-long submarine optical fiber,'' Proceedings of the National Academy of Sciences 116, 6684–6688 (2019).
 Si-Hui Tan, Baris I. Erkmen, Vittorio Giovannetti, Saikat Guha, Seth Lloyd, Lorenzo Maccone, Stefano Pirandola, and Jeffrey H. Shapiro, ``Quantum illumination with gaussian states,'' Phys. Rev. Lett. 101, 253601 (2008).
 Shahaf Asban, Konstantin E. Dorfman, and Shaul Mukamel, ``Quantum phase-sensitive diffraction and imaging using entangled photons,'' Proceedings of the National Academy of Sciences 116, 11673–11678 (2019), https://www.pnas.org/content/116/24/11673.full.pdf.
 J. Appel, P. J. Windpassinger, D. Oblak, U. B. Hoff, N. Kjaergaard, and E. S. Polzik, ``Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit,'' Proceedings of the National Academy of Sciences 106, 10960–10965 (2009).
 Gershon Kurizki, Patrice Bertet, Yuimaru Kubo, Klaus Mølmer, David Petrosyan, Peter Rabl, and Jörg Schmiedmayer, ``Quantum technologies with hybrid systems,'' Proceedings of the National Academy of Sciences 112, 3866–3873 (2015).
 S.-S. Li, G.-L. Long, F.-S. Bai, S.-L. Feng, and H.-Z. Zheng, ``Quantum computing,'' Proceedings of the National Academy of Sciences 98, 11847–11848 (2001).
 Mikkel V. Larsen, Xueshi Guo, Casper R. Breum, Jonas S. Neergaard-Nielsen, and Ulrik L. Andersen, ``Deterministic generation of a two-dimensional cluster state,'' Science 366, 369–372 (2019).
 Abhinav Kandala, Kristan Temme, Antonio D. Córcoles, Antonio Mezzacapo, Jerry M. Chow, and Jay M. Gambetta, ``Error mitigation extends the computational reach of a noisy quantum processor,'' Nature 567, 491–495 (2019).
 C. Flühmann, T. L. Nguyen, M. Marinelli, V. Negnevitsky, K. Mehta, and J. P. Home, ``Encoding a qubit in a trapped-ion mechanical oscillator,'' Nature 566, 513–517 (2019).
 P.W. Shor, ``Algorithms for quantum computation: discrete logarithms and factoring,'' in Proceedings 35th Annual Symposium on Foundations of Computer Science (IEEE Comput. Soc. Press).
 L. K. Grover; A fast quantum mechanical algorithm for database search, Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing. STOC '96. Philadelphia, Pennsylvania, USA: Association for Computing Machinery: 212–219 (1996).
 D. R. Simon; On the Power of Quantum Computation, Journal on Computing, 26(5), 1474–1483 (1997).
 L. Babai and P.G. Kimmel, ``Randomized simultaneous messages: solution of a problem of yao in communication complexity,'' (IEEE Comput. Soc).
 G. Brassard, R. Cleve, and A. Tapp, ``Cost of exactly simulating quantum entanglement with classical communication,'' Phys. Rev. Lett. 83, 1874–1877 (1999).
 J. Bowles, F. Hirsch, M. T. Quintino, and N. Brunner, ``Local hidden variable models for entangled quantum states using finite shared randomness,'' Phys. Rev. Lett. 114, 120401 (2015).
 Arup Roy, Amit Mukherjee, Tamal Guha, Sibasish Ghosh, Some Sankar Bhattacharya, and Manik Banik, ``Nonlocal correlations: Fair and unfair strategies in bayesian games,'' Phys. Rev. A 94, 032120 (2016).
 M. Banik, S. S. Bhattacharya, N. Ganguly, T. Guha, A. Mukherjee, A. Rai, and A. Roy, ``Two-qubit pure entanglement as optimal social welfare resource in bayesian game,'' Quantum 3, 185 (2019).
 C. L. Canonne, V. Guruswami, R. Meka, and M. Sudan, ``Communication with imperfectly shared randomness,'' IEEE Trans. Inf. Theory 63, 6799–6818 (2017).
 C. E. Shannon, ``A mathematical theory of communication,'' Bell System Technical Journal 27, 379–423 (1948).
 S. D. Bartlett, T. Rudolph, and R. W. Spekkens, ``Reference frames, superselection rules, and quantum information,'' Rev. Mod. Phys. 79, 555–609 (2007).
 K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, ``The classical-quantum boundary for correlations: Discord and related measures,'' Rev. Mod. Phys. 84, 1655–1707 (2012).
 F. G. S. L. Brandão, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, ``Resource theory of quantum states out of thermal equilibrium,'' Phys. Rev. Lett. 111, 250404 (2013).
 A. Grudka, K. Horodecki, M. Horodecki, P. Horodecki, R. Horodecki, P. Joshi, W. Kłobus, and A. Wójcik, ``Quantifying contextuality,'' Phys. Rev. Lett. 112, 120401 (2014).
 Á. Rivas, S. F Huelga, and M. B. Plenio, ``Quantum non-markovianity: characterization, quantification and detection,'' Rep. Prog. Phys. 77, 094001 (2014).
 V. Veitch, S. A. H. Mousavian, D. Gottesman, and J. Emerson, ``The resource theory of stabilizer quantum computation,'' New J. Phys. 16, 013009 (2014).
 A. Winter and D. Yang, ``Operational resource theory of coherence,'' Phys. Rev. Lett. 116, 120404 (2016).
 Elie Wolfe, David Schmid, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens, ``Quantifying bell: the resource theory of nonclassicality of common-cause boxes,'' Quantum 4, 280 (2020).
 D. Rosset, D. Schmid and F. Buschemi; Type-Independent Characterization of Spacelike Separated Resources, Phys. Rev. Lett. 125, 210402 (2020).
 L Henderson and V Vedral, ``Classical, quantum and total correlations,'' Journal of Physics A: Mathematical and General 34, 6899–6905 (2001).
 D. Cavalcanti, L. Aolita, S. Boixo, K. Modi, M. Piani, and A. Winter; Operational interpretations of quantum discord, Phys. Rev. A 83, 032324 (2011).
 A. Streltsov, H. Kampermann, and D. Bruß; Linking Quantum Discord to Entanglement in a Measurement, Phys. Rev. Lett. 106, 160401 (2011).
 T. K. C. Bobby and T. Paterek; Separable states improve protocols with finiterandomness, New J. Phys. 16, 093063 (2014).
 A. S. Holevo, ``Bounds for the quantity of information transmitted by a quantum communication channel,'' Problems of Information Transmission 9, 177–183 (1973).
 P. W. Shor, ``The quantum channel capacity and coherent information,'' Lecture notes,MSRIWorkshop on Quantum Computation -, – (2002).
 F. G. S. L. Brandão and G. Gour, ``Reversible framework for quantum resource theories,'' Phys. Rev. Lett. 115, 070503 (2015).
 K. Kraus, States, Effects, and Operations Fundamental Notions of Quantum Theory, edited by K. Kraus, A. Böhm, J. D. Dollard, and W. H. Wootters (Springer Berlin Heidelberg, 1983).
 Michael J. W. Hall, ``Local deterministic model of singlet state correlations based on relaxing measurement independence,'' Phys. Rev. Lett. 105, 250404 (2010).
 Jonathan Barrett and Nicolas Gisin, ``How much measurement independence is needed to demonstrate nonlocality?'' Phys. Rev. Lett. 106, 100406 (2011).
 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).
 Gaurav Saxena and Gilad Gour, "Quantifying multiqubit magic channels with completely stabilizer-preserving operations", Physical Review A 106 4, 042422 (2022).
 Govind Lal Sidhardh, Mir Alimuddin, and Manik Banik, "Exploring superadditivity of coherent information of noisy quantum channels through genetic algorithms", Physical Review A 106 1, 012432 (2022).
 Dashiell LP Vitullo, Trevor Cook, Daniel E Jones, Lisa M Scott, Andrew Toth, and Brian T Kirby, "Simulating quantum key distribution in fiber-based quantum networks", The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology 154851292311549 (2023).
The above citations are from Crossref's cited-by service (last updated successfully 2023-11-29 15:30:36) and SAO/NASA ADS (last updated successfully 2023-11-29 15:30:37). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.