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Quantum Advantage in Non-Interactive Source Simulation (2402.00242v2)

Published 31 Jan 2024 in quant-ph, cs.IT, and math.IT

Abstract: This work considers the non-interactive source simulation problem (NISS). In the standard NISS scenario, a pair of distributed agents, Alice and Bob, observe a distributed binary memoryless source $(Xd,Yd)$ generated based on joint distribution $P_{X,Y}$. The agents wish to produce a pair of discrete random variables $(U_d,V_d)$ with joint distribution $P_{U_d,V_d}$, such that $P_{U_d,V_d}$ converges in total variation distance to a target distribution $Q_{U,V}$. Two variations of the standard NISS scenario are considered. In the first variation, in addition to $(Xd,Yd)$ the agents have access to a shared Bell state. The agents each measure their respective state, using a measurement of their choice, and use its classical output along with $(Xd,Yd)$ to simulate the target distribution. This scenario is called the entanglement-assisted NISS (EA-NISS). In the second variation, the agents have access to a classical common random bit $Z$, in addition to $(Xd,Yd)$. This scenario is called the classical common randomness NISS (CR-NISS). It is shown that for binary-output NISS scenarios, the set of feasible distributions for EA-NISS and CR-NISS are equal with each other. Hence, there is not quantum advantage in these EA-NISS scenarios. For non-binary output NISS scenarios, it is shown through an example that there are distributions that are feasible in EA-NISS but not in CR-NISS. This shows that there is a quantum advantage in non-binary output EA-NISS.

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References (37)
  1. B. Ghazi, P. Kamath, and M. Sudan, “Decidability of non-interactive simulation of joint distributions,” in 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).   IEEE, 2016, pp. 545–554.
  2. B. Ghazi, P. Kamath, and P. Raghavendra, “Dimension reduction for polynomials over gaussian space and applications,” arXiv preprint arXiv:1708.03808, 2017.
  3. A. De, E. Mossel, and J. Neeman, “Non interactive simulation of correlated distributions is decidable,” in Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms.   SIAM, 2018, pp. 2728–2746.
  4. H. A. Khorasgani, H. K. Maji, and H. H. Nguyen, “Decidability of secure non-interactive simulation of doubly symmetric binary source,” Cryptology ePrint Archive, 2021.
  5. K. Bhushan, A. K. Misra, V. Narayanan, and M. Prabhakaran, “Secure non-interactive reducibility is decidable,” in Theory of Cryptography: 20th International Conference, TCC 2022, Chicago, IL, USA, November 7–10, 2022, Proceedings, Part II.   Springer, 2023, pp. 408–437.
  6. L. Yu, V. Y. Tan et al., “Common information, noise stability, and their extensions,” Foundations and Trends® in Communications and Information Theory, vol. 19, no. 2, pp. 107–389, 2022.
  7. M. Sudan, H. Tyagi, and S. Watanabe, “Communication for generating correlation: A unifying survey,” IEEE Transactions on Information Theory, vol. 66, no. 1, pp. 5–37, 2019.
  8. F. S. Chaharsooghi and S. S. Pradhan, “On the correlation between boolean functions of sequences of random variables,” in 2017 IEEE International Symposium on Information Theory (ISIT), 2017, pp. 1301–1305.
  9. F. Shirani and S. S. Pradhan, “On the sub-optimality of single-letter coding over networks,” IEEE Transactions on Information Theory, vol. 65, no. 10, pp. 6115–6135, 2019.
  10. F. Shirani and M. Heidari, “On non-interactive source simulation via fourier transform,” in 2023 IEEE Information Theory Workshop (ITW).   IEEE, 2023, pp. 371–376.
  11. C. Cachin and V. Shoup, “Random oracles in constantinople: Practical asynchronous byzantine agreement using,” in Proceedings of the 19th ACM Symposium on Principles of Distributed Computing, no, 2000, pp. 1–26.
  12. M. O. Rabin, “Randomized byzantine generals,” in 24th annual symposium on foundations of computer science (sfcs 1983).   IEEE, 1983, pp. 403–409.
  13. I. Bentov, R. Pass, and E. Shi, “Snow white: Provably secure proofs of stake.” IACR Cryptol. ePrint Arch., vol. 2016, no. 919, 2016.
  14. Y. Gilad, R. Hemo, S. Micali, G. Vlachos, and N. Zeldovich, “Algorand: Scaling byzantine agreements for cryptocurrencies,” in Proceedings of the 26th symposium on operating systems principles, 2017, pp. 51–68.
  15. S. Das, V. J. Ribeiro, and A. Anand, “Yoda: Enabling computationally intensive contracts on blockchains with byzantine and selfish nodes,” arXiv preprint arXiv:1811.03265, 2018.
  16. S. Goel, M. Robson, M. Polte, and E. Sirer, “Herbivore: A scalable and efficient protocol for anonymous communication,” Cornell University, Tech. Rep., 2003.
  17. R. Dingledine, N. Mathewson, and P. Syverson, “Tor: The second-generation onion router,” Naval Research Lab Washington DC, Tech. Rep., 2004.
  18. J. Bonneau, J. Clark, and S. Goldfeder, “On bitcoin as a public randomness source,” Cryptology ePrint Archive, 2015.
  19. R. Ahlswede and I. Csiszár, “Common randomness in information theory and cryptography. i. secret sharing,” IEEE Transactions on Information Theory, vol. 39, no. 4, pp. 1121–1132, 1993.
  20. U. M. Maurer, “Secret key agreement by public discussion from common information,” IEEE transactions on information theory, vol. 39, no. 3, pp. 733–742, 1993.
  21. T. Baigneres, C. Delerablée, M. Finiasz, L. Goubin, T. Lepoint, and M. Rivain, “Trap me if you can–million dollar curve,” Cryptology ePrint Archive, 2015.
  22. S. Kamath and V. Anantharam, “On non-interactive simulation of joint distributions,” IEEE Transactions on Information Theory, vol. 62, no. 6, pp. 3419–3435, 2016.
  23. J. Li and M. Médard, “Boolean functions: noise stability, non-interactive correlation distillation, and mutual information,” IEEE Transactions on Information Theory, vol. 67, no. 2, pp. 778–789, 2020.
  24. H. S. Witsenhausen, “On sequences of pairs of dependent random variables,” SIAM Journal on Applied Mathematics, vol. 28, no. 1, pp. 100–113, 1975.
  25. M. B. Plenio and S. Virmani, “An introduction to entanglement measures,” 2005.
  26. E. Chitambar and G. Gour, “Quantum resource theories,” 2018.
  27. H.-Y. Huang, R. Kueng, and J. Preskill, “Information-theoretic bounds on quantum advantage in machine learning,” Physical Review Letters, vol. 126, no. 19, p. 190505, 2021.
  28. H.-Y. Huang, M. Broughton, M. Mohseni, R. Babbush, S. Boixo, H. Neven, and J. R. McClean, “Power of data in quantum machine learning,” Nature communications, vol. 12, no. 1, p. 2631, 2021.
  29. C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal, “Entanglement-assisted capacity of a quantum channel and the reverse shannon theorem,” IEEE transactions on Information Theory, vol. 48, no. 10, pp. 2637–2655, 2002.
  30. M.-H. Hsieh and M. M. Wilde, “Trading classical communication, quantum communication, and entanglement in quantum shannon theory,” IEEE Transactions on Information Theory, vol. 56, no. 9, pp. 4705–4730, 2010.
  31. C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal, “Entanglement-assisted classical capacity of noisy quantum channels,” Physical Review Letters, vol. 83, no. 15, p. 3081, 1999.
  32. F. Leditzky, M. A. Alhejji, J. Levin, and G. Smith, “Playing games with multiple access channels,” Nature communications, vol. 11, no. 1, p. 1497, 2020.
  33. A. Seshadri, F. Leditzky, V. Siddhu, and G. Smith, “On the separation of correlation-assisted sum capacities of multiple access channels,” IEEE Transactions on Information Theory, 2023.
  34. U. Pereg, C. Deppe, and H. Boche, “The multiple-access channel with entangled transmitters,” arXiv preprint arXiv:2303.10456, 2023.
  35. I. Devetak, A. W. Harrow, and A. J. Winter, “A resource framework for quantum shannon theory,” IEEE Transactions on Information Theory, vol. 54, no. 10, pp. 4587–4618, 2008.
  36. M. A. Nielsen, “Conditions for a class of entanglement transformations,” Physical Review Letters, vol. 83, no. 2, p. 436, 1999.
  37. J. Von Neumann, “Various techniques used in connection with random digits,” Appl. Math Ser, vol. 12, no. 36-38, p. 3, 1951.

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