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Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems (2306.13054v2)

Published 22 Jun 2023 in quant-ph, cs.CR, cs.IT, cs.LG, and math.IT

Abstract: We propose a versatile privacy framework for quantum systems, termed quantum pufferfish privacy (QPP). Inspired by classical pufferfish privacy, our formulation generalizes and addresses limitations of quantum differential privacy by offering flexibility in specifying private information, feasible measurements, and domain knowledge. We show that QPP can be equivalently formulated in terms of the Datta-Leditzky information spectrum divergence, thus providing the first operational interpretation thereof. We reformulate this divergence as a semi-definite program and derive several properties of it, which are then used to prove convexity, composability, and post-processing of QPP mechanisms. Parameters that guarantee QPP of the depolarization mechanism are also derived. We analyze the privacy-utility tradeoff of general QPP mechanisms and, again, study the depolarization mechanism as an explicit instance. The QPP framework is then applied to privacy auditing for identifying privacy violations via a hypothesis testing pipeline that leverages quantum algorithms. Connections to quantum fairness and other quantum divergences are also explored and several variants of QPP are examined.

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References (70)
  1. C. Dwork, F. McSherry, K. Nissim, and A. Smith, “Calibrating noise to sensitivity in private data analysis,” in Proceedings of Conference on Theory of Cryptography, TCC, 2006, pp. 265–284.
  2. C. Dwork and A. Roth, “The algorithmic foundations of differential privacy,” Foundations and Trends in Theoretical Computer Science (FnT-TCS), vol. 9, no. 3-4, pp. 211–407, 2014.
  3. D. Kifer and A. Machanavajjhala, “Pufferfish: A framework for mathematical privacy definitions,” ACM Transactions on Database Systems, vol. 39, no. 1, pp. 1–36, 2014.
  4. S. Song, Y. Wang, and K. Chaudhuri, “Pufferfish privacy mechanisms for correlated data,” in Proceedings of ACM SIGMOD, 2017, pp. 1291–1306.
  5. W. Zhang, O. Ohrimenko, and R. Cummings, “Attribute privacy: Framework and mechanisms,” in Proceedings of ACM Conference on Fairness, Accountability, and Transparency, 2022, pp. 757–766.
  6. P. Cuff and L. Yu, “Differential privacy as a mutual information constraint,” in Proceedings of ACM SIGSAC Conference on Computer and Communications Security, 2016, pp. 43–54.
  7. T. Nuradha and Z. Goldfeld, “An information-theoretic characterization of pufferfish privacy,” in Proceedings of IEEE International Symposium on Information Theory (ISIT).   IEEE, 2022, pp. 2005–2010.
  8. L. Zhou and M. Ying, “Differential privacy in quantum computation,” in Proceedings of IEEE Computer Security Foundations Symposium (CSF).   IEEE, 2017, pp. 249–262.
  9. S. Aaronson and G. N. Rothblum, “Gentle measurement of quantum states and differential privacy,” in Proceedings of ACM SIGACT Symposium on Theory of Computing, 2019, pp. 322–333.
  10. C. Hirche, C. Rouzé, and D. S. França, “Quantum differential privacy: An information theory perspective,” IEEE Transactions on Information Theory, 2023, arXiv:2202.10717.
  11. S. Arunachalam, Y. Quek, and J. Smolin, “Private learning implies quantum stability,” arXiv preprint arXiv:2102.07171, 2021.
  12. S. Arunachalam, Y. Quek, and J. A. Smolin, “Private learning implies quantum stability,” Advances in Neural Information Processing Systems, vol. 34, pp. 20 503–20 515, 2021.
  13. Y. Du, M.-H. Hsieh, T. Liu, D. Tao, and N. Liu, “Quantum noise protects quantum classifiers against adversaries,” Physical Review Research, vol. 3, no. 2, p. 023153, 2021.
  14. N. Datta and F. Leditzky, “Second-order asymptotics for source coding, dense coding, and pure-state entanglement conversions,” IEEE Transactions on Information Theory, vol. 61, no. 1, pp. 582–608, 2014.
  15. R. Bassily, A. Groce, J. Katz, and A. Smith, “Coupled-worlds privacy: Exploiting adversarial uncertainty in statistical data privacy,” in Proceedings of IEEE Symposium on Foundations of Computer Science.   IEEE, 2013, pp. 439–448.
  16. B. M. Terhal, D. P. DiVincenzo, and D. W. Leung, “Hiding bits in bell states,” Physical Review Letters, vol. 86, no. 25, pp. 5807–5810, Jun. 2001.
  17. D. P. DiVincenzo, D. W. Leung, and B. M. Terhal, “Quantum data hiding,” IEEE Transactions on Information Theory, vol. 48, no. 3, pp. 580–598, 2002.
  18. T. Eggeling and R. F. Werner, “Hiding classical data in multipartite quantum states,” Physical Review Letters, vol. 89, no. 9, p. 097905, Aug. 2002.
  19. P. Hayden, D. Leung, P. W. Shor, and A. Winter, “Randomizing quantum states: Constructions and applications,” Communications in Mathematical Physics, vol. 250, no. 2, pp. 371–391, 2004.
  20. P. Hayden, D. Leung, and G. Smith, “Multiparty data hiding of quantum information,” Physical Review A, vol. 71, no. 6, p. 062339, Jun. 2005.
  21. C. Lupo, M. M. Wilde, and S. Lloyd, “Quantum data hiding in the presence of noise,” IEEE Transactions on Information Theory, vol. 62, no. 6, pp. 3745–3756, 2016.
  22. L. Lami, C. Palazuelos, and A. Winter, “Ultimate data hiding in quantum mechanics and beyond,” Communications in Mathematical Physics, vol. 361, no. 2, pp. 661–708, 2018.
  23. T. Murakami and Y. Kawamoto, “Utility-optimized local differential privacy mechanisms for distribution estimation.” in Proceedings of USENIX Security Symposium, 2019, pp. 1877–1894.
  24. J. Guan, W. Fang, and M. Ying, “Verifying fairness in quantum machine learning,” in Proceedings of International Conference on Computer Aided Verification.   Springer, 2022, pp. 408–429.
  25. E. Perrier, “Quantum fair machine learning,” in Proceedings of AAAI/ACM Conference on AI, Ethics, and Society, 2021, pp. 843–853.
  26. S. Khatri and M. M. Wilde, “Principles of quantum communication theory: A modern approach,” arXiv preprint arXiv:2011.04672v1, 2020.
  27. N. Sharma and N. A. Warsi, “On the strong converses for the quantum channel capacity theorems,” arXiv:1205.1712, May 2012.
  28. A. Uhlmann, “The ‘Transition Probability’ in the State Space of a *-Algebra,” Reports on Mathematical Physics, vol. 9, pp. 273–279, 1976.
  29. A. Kitaev, “Quantum computations: algorithms and error correction,” Russian Mathematical Surveys, vol. 52, pp. 1191–1249, 1997.
  30. D. Petz, “Quasi-entropies for States of a von Neumann Algebra,” Publications of the Research Institute for Mathematical Sciences, vol. 21, pp. 787–800, 1985.
  31. ——, “Quasi-entropies for finite quantum systems,” Reports in Mathematical Physics, vol. 23, pp. 57–65, 1986.
  32. M. Müller-Lennert, F. Dupuis, O. Szehr, S. Fehr, and M. Tomamichel, “On quantum Rényi entropies: A new generalization and some properties,” Journal of Mathematical Physics, vol. 54, no. 12, p. 122203, 2013.
  33. M. M. Wilde, A. Winter, and D. Yang, “Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Rényi relative entropy,” Communications in Mathematical Physics, vol. 331, pp. 593–622, 2014.
  34. R. L. Frank and E. H. Lieb, “Monotonicity of a relative Rényi entropy,” Journal of Mathematical Physics, vol. 54, p. 122201, 2013.
  35. M. M. Wilde, “Optimized quantum f𝑓fitalic_f-divergences and data processing,” Journal of Physics A, vol. 51, p. 374002, 2018.
  36. N. Datta, “Min-and max-relative entropies and a new entanglement monotone,” IEEE Transactions on Information Theory, vol. 55, no. 6, pp. 2816–2826, 2009.
  37. X. Wang and M. M. Wilde, “Resource theory of asymmetric distinguishability,” Physical Review Research, vol. 1, no. 3, p. 033170, 2019.
  38. A. C. Thompson, “On certain contraction mappings in a partially ordered vector space.” Proceedings of the American Mathematical Society, vol. 14, no. 3, pp. 438–443, 1963.
  39. R. Salzmann, N. Datta, G. Gour, X. Wang, and M. M. Wilde, “Symmetric distinguishability as a quantum resource,” New Journal of Physics, vol. 23, no. 8, p. 083016, 2021.
  40. B. Regula, L. Lami, and M. M. Wilde, “Postselected quantum hypothesis testing,” arXiv preprint arXiv:2209.10550, 2022.
  41. D. Kifer and B.-R. Lin, “An axiomatic view of statistical privacy and utility,” Journal of Privacy and Confidentiality, vol. 4, no. 1, 2012.
  42. W. Matthews, S. Wehner, and A. Winter, “Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding,” Communications in Mathematical Physics, vol. 291, no. 3, pp. 813–843, 2009.
  43. E. B. Davies and J. T. Lewis, “An operational approach to quantum probability,” Communications in Mathematical Physics, vol. 17, no. 3, pp. 239–260, September 1970.
  44. M. Ozawa, “Quantum measuring processes of continuous observables,” Journal of Mathematical Physics, vol. 25, no. 1, pp. 79–87, 1984.
  45. Ú. Erlingsson, V. Pihur, and A. Korolova, “Rappor: Randomized aggregatable privacy-preserving ordinal response,” in Proceedings of ACM SIGSAC conference on computer and communications security, 2014, pp. 1054–1067.
  46. J. Watrous, “Semidefinite programs for completely bounded norms,” Theory of Computing, vol. 5, no. 11, pp. 217–238, 2009.
  47. M. Horodecki, P. Horodecki, and R. Horodecki, “General teleportation channel, singlet fraction, and quasidistillation,” Physical Review A, vol. 60, pp. 1888–1898, Sep. 1999.
  48. Z. Ding, Y. Wang, G. Wang, D. Zhang, and D. Kifer, “Detecting violations of differential privacy,” in Proceedings of ACM SIGSAC Conference on Computer and Communications Security, 2018, pp. 475–489.
  49. M. Jagielski, J. Ullman, and A. Oprea, “Auditing differentially private machine learning: How private is private SGD?” Advances in Neural Information Processing Systems, vol. 33, pp. 22 205–22 216, 2020.
  50. C. Domingo-Enrich and Y. Mroueh, “Auditing differential privacy in high dimensions with the kernel quantum Rényi divergence,” arXiv preprint arXiv:2205.13941, 2022.
  51. T. Nuradha and Z. Goldfeld, “Pufferfish privacy: An information-theoretic study,” arXiv preprint arXiv:2210.12612, 2022.
  52. J. Watrous, “Limits on the power of quantum statistical zero-knowledge,” Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, pp. 459–468, November 2002, arXiv:quant-ph/0202111.
  53. ——, “Zero-knowledge against quantum attacks,” SIAM Journal on Computing, vol. 39, no. 1, pp. 25–58, 2009, arXiv:quant-ph/0511020.
  54. S. Rethinasamy, R. Agarwal, K. Sharma, and M. M. Wilde, “Estimating distinguishability measures on quantum computers,” arXiv preprint arXiv:2108.08406, 2021.
  55. R. Chen, Z. Song, X. Zhao, and X. Wang, “Variational quantum algorithms for trace distance and fidelity estimation,” Quantum Science and Technology, vol. 7, no. 1, pp. 015–019, 2021.
  56. Q. Wang and Z. Zhang, “Fast quantum algorithms for trace distance estimation,” arXiv preprint arXiv:2301.06783, 2023.
  57. M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, “Variational quantum algorithms,” Nature Reviews Physics, vol. 3, pp. 625–644, Aug. 2021, arXiv:2012.09265.
  58. K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, W.-K. Mok, S. Sim, L.-C. Kwek, and A. Aspuru-Guzik, “Noisy intermediate-scale quantum (NISQ) algorithms,” Reviews of Modern Physics, vol. 94, no. 1, p. 015004, Feb. 2022, arXiv:2101.08448.
  59. A. Gilyén, Y. Su, G. H. Low, and N. Wiebe, “Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics,” in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, 2019, pp. 193–204.
  60. D. Aharonov, V. Jones, and Z. Landau, “A polynomial quantum algorithm for approximating the Jones polynomial,” Algorithmica, vol. 55, no. 3, pp. 395–421, 2009.
  61. S. Lloyd, M. Mohseni, and P. Rebentrost, “Quantum principal component analysis,” Nature Physics, vol. 10, no. 9, pp. 631–633, Jul. 2014.
  62. E. H. Lieb and M. B. Ruskai, “Proof of the strong subadditivity of quantum-mechanical entropy,” Journal of Mathematical Physics, vol. 14, no. 12, pp. 1938–1941, December 1973.
  63. K. M. R. Audenaert, “A sharp continuity estimate for the von Neumann entropy,” Journal of Physics A: Mathematical and Theoretical, vol. 40, no. 28, p. 8127, July 2007, arXiv:quant-ph/0610146.
  64. I. Mironov, “Rényi differential privacy,” in Proceedings of IEEE computer security foundations symposium (CSF), 2017, pp. 263–275.
  65. M. Bun and T. Steinke, “Concentrated differential privacy: Simplifications, extensions, and lower bounds,” in Proceedings of Theory of Cryptography Conference.   Springer, 2016, pp. 635–658.
  66. Q. Wang, J. Guan, J. Liu, Z. Zhang, and M. Ying, “New quantum algorithms for computing quantum entropies and distances,” arXiv preprint arXiv:2203.13522, 2022.
  67. M. Berta, O. Fawzi, and M. Tomamichel, “On variational expressions for quantum relative entropies,” Letters in Mathematical Physics, vol. 107, pp. 2239–2265, 2017.
  68. K. Matsumoto, “A new quantum version of f𝑓fitalic_f-divergence,” 2013.
  69. ——, “A new quantum version of f𝑓fitalic_f-divergence,” in Reality and Measurement in Algebraic Quantum Theory, M. Ozawa, J. Butterfield, H. Halvorson, M. Rédei, Y. Kitajima, and F. Buscemi, Eds., vol. 261.   Singapore: Springer Singapore, 2018, pp. 229–273, series Title: Springer Proceedings in Mathematics & Statistics.
  70. F. Hiai and M. Mosonyi, “Different quantum f𝑓fitalic_f-divergences and the reversibility of quantum operations,” Reviews in Mathematical Physics, vol. 29, no. 07, p. 1750023, 2017.
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