A Computational Separation Between Quantum No-Cloning and No-Telegraphing

Authors Barak Nehoran , Mark Zhandry

Thumbnail PDF


  • Filesize: 0.83 MB
  • 23 pages

Document Identifiers

Author Details

Barak Nehoran
  • Princeton University, NJ, USA
Mark Zhandry
  • NTT Research, Sunnyvale, CA, USA

Cite AsGet BibTex

Barak Nehoran and Mark Zhandry. A Computational Separation Between Quantum No-Cloning and No-Telegraphing. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 82:1-82:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Two of the fundamental no-go theorems of quantum information are the no-cloning theorem (that it is impossible to make copies of general quantum states) and the no-teleportation theorem (the prohibition on telegraphing, or sending quantum states over classical channels without pre-shared entanglement). They are known to be equivalent, in the sense that a collection of quantum states is telegraphable if and only if it is clonable. Our main result suggests that this is not the case when computational efficiency is considered. We give a collection of quantum states and quantum oracles relative to which these states are efficiently clonable but not efficiently telegraphable. Given that the opposite scenario is impossible (states that can be telegraphed can always trivially be cloned), this gives the most complete quantum oracle separation possible between these two important no-go properties. We additionally study the complexity class clonableQMA, a subset of QMA whose witnesses are efficiently clonable. As a consequence of our main result, we give a quantum oracle separation between clonableQMA and the class QCMA, whose witnesses are restricted to classical strings. We also propose a candidate oracle-free promise problem separating these classes. We finally demonstrate an application of clonable-but-not-telegraphable states to cryptography, by showing how such states can be used to protect against key exfiltration.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum query complexity
  • Theory of computation → Oracles and decision trees
  • Theory of computation → Complexity classes
  • Theory of computation → Cryptographic primitives
  • Theory of computation → Quantum complexity theory
  • Cloning
  • telegraphing
  • no-cloning theorem
  • oracle separations


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Scott Aaronson. Quantum copy-protection and quantum money. Proceedings of the Annual IEEE Conference on Computational Complexity, October 2011. Google Scholar
  2. Scott Aaronson and Paul Christiano. Quantum money from hidden subspaces. In Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing, STOC '12, pages 41-60, New York, NY, USA, 2012. Association for Computing Machinery. Google Scholar
  3. Scott Aaronson and Greg Kuperberg. Quantum versus classical proofs and advice. In Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07), pages 115-128. IEEE, 2007. Google Scholar
  4. Dorit Aharonov and Tomer Naveh. Quantum NP - a survey, 2002. URL: https://arxiv.org/abs/quant-ph/0210077.
  5. A. Ambainis, A. Rosmanis, and D. Unruh. Quantum attacks on classical proof systems: The hardness of quantum rewinding. In 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS), pages 474-483, Los Alamitos, CA, USA, October 2014. IEEE Computer Society. Google Scholar
  6. Ryan Amos, Marios Georgiou, Aggelos Kiayias, and Mark Zhandry. One-shot signatures and applications to hybrid quantum/classical authentication. In Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020, pages 255-268, New York, NY, USA, 2020. Association for Computing Machinery. Google Scholar
  7. Prabhanjan Ananth and Rolando L. La Placa. Secure software leasing. In Anne Canteaut and François-Xavier Standaert, editors, Advances in Cryptology - EUROCRYPT 2021, pages 501-530, Cham, 2021. Springer International Publishing. Google Scholar
  8. James Bartusek, Andrea Coladangelo, Dakshita Khurana, and Fermi Ma. One-way functions imply secure computation in a quantum world. In Advances in Cryptology – CRYPTO 2021: 41st Annual International Cryptology Conference, CRYPTO 2021, Virtual Event, August 16–20, 2021, Proceedings, Part I, pages 467-496, Berlin, Heidelberg, 2021. Springer-Verlag. Google Scholar
  9. James Bartusek and Giulio Malavolta. Indistinguishability obfuscation of null quantum circuits and applications. In ITCS 2022, 2022. Google Scholar
  10. Mihir Bellare and Wei Dai. Defending against key exfiltration: Efficiency improvements for big-key cryptography via large-alphabet subkey prediction. In Bhavani Thuraisingham, David Evans, Tal Malkin, and Dongyan Xu, editors, Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, CCS 2017, Dallas, TX, USA, October 30 - November 03, 2017, pages 923-940. ACM, 2017. Google Scholar
  11. Mihir Bellare, Daniel Kane, and Phillip Rogaway. Big-key symmetric encryption: Resisting key exfiltration. In Matthew Robshaw and Jonathan Katz, editors, Advances in Cryptology - CRYPTO 2016, pages 373-402, Berlin, Heidelberg, 2016. Springer Berlin Heidelberg. Google Scholar
  12. Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh V. Vazirani. Strengths and weaknesses of quantum computing. SIAM J. Comput., 26(5):1510-1523, 1997. URL: https://doi.org/10.1137/S0097539796300933.
  13. Charles H Bennett and Gilles Brassard. Quantum cryptography: Public key distribution and coin tossing. In Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 1984, 1984. Google Scholar
  14. Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels. Phys. Rev. Lett., 70:1895-1899, March 1993. URL: https://doi.org/10.1103/PhysRevLett.70.1895.
  15. Andrea Coladangelo, Jiahui Liu, Qipeng Liu, and Mark Zhandry. Hidden cosets and applications to unclonable cryptography. In Tal Malkin and Chris Peikert, editors, CRYPTO 2021, Part I, volume 12825 of LNCS, pages 556-584. Springer, Heidelberg, August 2021. Google Scholar
  16. D. Dieks. Communication by EPR devices. Phys. Lett. A, 1982. Google Scholar
  17. Edward Farhi, David Gosset, Avinatan Hassidim, Andrew Lutomirski, and Peter Shor. Quantum money from knots. In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, ITCS '12, pages 276-289, New York, NY, USA, 2012. Association for Computing Machinery. Google Scholar
  18. Bill Fefferman and Shelby Kimmel. Quantum vs. classical proofs and subset verification. In 43rd International Symposium on Mathematical Foundations of Computer Science, page 1, 2018. Google Scholar
  19. Marios Georgiou and Mark Zhandry. Unclonable decryption keys. Cryptology ePrint Archive, Paper 2020/877, 2020. URL: https://eprint.iacr.org/2020/877.
  20. Alex B. Grilo, Huijia Lin, Fang Song, and Vinod Vaikuntanathan. Oblivious transfer is in MiniQCrypt. In Advances in Cryptology – EUROCRYPT 2021: 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, October 17–21, 2021, Proceedings, Part II, pages 531-561, Berlin, Heidelberg, 2021. Springer-Verlag. Google Scholar
  21. Yassine Hamoudi and Frédéric Magniez. Quantum time-space tradeoff for finding multiple collision pairs. ACM Trans. Comput. Theory, 15(1-2):1-22, 2023. URL: https://doi.org/10.1145/3589986.
  22. Daniel Harlow and Patrick Hayden. Quantum computation vs. firewalls. Journal of High Energy Physics, 2013, January 2013. Google Scholar
  23. Xingjian Li, Qipeng Liu, Angelos Pelecanos, and Takashi Yamakawa. Classical vs quantum advice under classically-accessible oracle, 2023. URL: https://arxiv.org/abs/2303.04298.
  24. Jiahui Liu, Qipeng Liu, Luowen Qian, and Mark Zhandry. Collusion resistant copy-protection for watermarkable functionalities. In Eike Kiltz and Vinod Vaikuntanathan, editors, TCC 2022, Part I, volume 13747 of LNCS, pages 294-323. Springer, Heidelberg, November 2022. Google Scholar
  25. Hoi-Kwong Lo and H. Chau. Is quantum bit commitment really possible? Physical Review Letters, 78, August 1998. Google Scholar
  26. Dominic Mayers. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters, 78, May 1996. Google Scholar
  27. Tal Moran and Daniel Wichs. Incompressible encodings. In Daniele Micciancio and Thomas Ristenpart, editors, Advances in Cryptology - CRYPTO 2020, pages 494-523, Cham, 2020. Springer International Publishing. Google Scholar
  28. Anand Natarajan and Chinmay Nirkhe. A distribution testing oracle separation between QMA and QCMA, 2023. URL: https://arxiv.org/abs/2210.15380.
  29. Barak Nehoran and Mark Zhandry. A computational separation between quantum no-cloning and no-telegraphing, 2023. URL: https://arxiv.org/abs/2302.01858.
  30. James L. Park. The concept of transition in quantum mechanics. Foundations of Physics, 1970. Google Scholar
  31. Roy Radian and Or Sattath. Semi-quantum money. J. Cryptol., 35(2):8, 2022. URL: https://doi.org/10.1007/S00145-021-09418-8.
  32. Omri Shmueli. Public-key quantum money with a classical bank. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022, pages 790-803, New York, NY, USA, 2022. Association for Computing Machinery. Google Scholar
  33. R. F. Werner. Optimal cloning of pure states. Physical Review A, 58(3):1827-1832, September 1998. URL: https://doi.org/10.1103/physreva.58.1827.
  34. William K. Wootters and Wojciech Zurek. A single quantum cannot be cloned. Nature, 299:802-803, 1982. Google Scholar
  35. Horace P. Yuen. Amplification of quantum states and noiseless photon amplifiers. Physics Letters A, 113(8):405-407, 1986. URL: https://doi.org/10.1016/0375-9601(86)90660-2.
  36. Mark Zhandry. A note on the quantum collision and set equality problems. Quantum Info. Comput., 15(7-8):557-567, May 2015. Google Scholar
  37. Mark Zhandry. Quantum lightning never strikes the same state twice. In Yuval Ishai and Vincent Rijmen, editors, Advances in Cryptology - EUROCRYPT 2019, pages 408-438, Cham, 2019. Springer International Publishing. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail