Photonic quantum data locking

Zixin Huang1, Peter P. Rohde2, Dominic W. Berry3, Pieter Kok1, Jonathan P. Dowling4,5,6,7, and Cosmo Lupo1

1Department of Physics & Astronomy, University of Sheffield, UK
2Centre for Quantum Software & Information (QSI), Faculty of Engineering & Information Technology University of Technology Sydney, NSW 2007, Australia
3Department of Physics and Astronomy, Macquarie University, Sydney, New South Wales 2109, Australia
4Hearne Institute for Theoretical Physics and Department of Physics & Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
5National Institute of Information and Communications Technology, 4-2-1, Nukui-Kitamachi, Koganei, Tokyo 184-8795, Japan
6NYU-ECNU Institute of Physics at NYU Shanghai, Shanghai 200062, China
7CAS-Alibaba Quantum Computing Laboratory, USTC, Shanghai 201315, China

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Quantum data locking is a quantum phenomenon that allows us to encrypt a long message with a small secret key with information-theoretic security. This is in sharp contrast with classical information theory where, according to Shannon, the secret key needs to be at least as long as the message. Here we explore photonic architectures for quantum data locking, where information is encoded in multi-photon states and processed using multi-mode linear optics and photo-detection, with the goal of extending an initial secret key into a longer one. The secret key consumption depends on the number of modes and photons employed. In the no-collision limit, where the likelihood of photon bunching is suppressed, the key consumption is shown to be logarithmic in the dimensions of the system. Our protocol can be viewed as an application of the physics of Boson Sampling to quantum cryptography. Experimental realisations are challenging but feasible with state-of-the-art technology, as techniques recently used to demonstrate Boson Sampling can be adapted to our scheme (e.g., Phys. Rev. Lett. 123, 250503, 2019).


This paper is dedicated to the memory of Professor Jonathan P. Dowling.



We propose a private-key encryption protocol exploiting Boson-Sampling and prove its security against an eavesdropper with unlimited quantum computation power but imperfect quantum memory. Our scheme is secure even for small numbers of modes and photons and robust against noise and loss, therefore representing the first practical application of Boson-Sampling for communications. Boson-Sampling offers more efficiency than quantum key distribution (QKD) with an exponential scale-up of the communication capacity using polynomial resources.

► BibTeX data

► References

[1] Claude E Shannon. Communication theory of secrecy systems. Bell system technical journal, 28 (4): 656–715, 1949.

[2] David P. DiVincenzo, Michał Horodecki, Debbie W. Leung, John A. Smolin, and Barbara M. Terhal. Locking classical correlations in quantum states. Phys. Rev. Lett., 92: 067902, Feb 2004. 10.1103/​PhysRevLett.92.067902.

[3] Saikat Guha, Patrick Hayden, Hari Krovi, Seth Lloyd, Cosmo Lupo, Jeffrey H. Shapiro, Masahiro Takeoka, and Mark M. Wilde. Quantum enigma machines and the locking capacity of a quantum channel. Phys. Rev. X, 4: 011016, Jan 2014. 10.1103/​PhysRevX.4.011016.

[4] Cosmo Lupo and Seth Lloyd. Quantum-locked key distribution at nearly the classical capacity rate. Phys. Rev. Lett., 113: 160502, Oct 2014. 10.1103/​PhysRevLett.113.160502.

[5] Cosmo Lupo. Quantum data locking for secure communication against an eavesdropper with time-limited storage. Entropy, 17 (5): 3194–3204, 2015.

[6] Patrick Hayden, Debbie Leung, Peter W Shor, and Andreas Winter. Randomizing quantum states: Constructions and applications. Communications in Mathematical Physics, 250 (2): 371–391, 2004. 10.1007/​s00220-004-1087-6.

[7] Omar Fawzi, Patrick Hayden, and Pranab Sen. From low-distortion norm embeddings to explicit uncertainty relations and efficient information locking. Journal of the ACM, 60: 44, 2013. 10.1145/​2518131.

[8] Stephanie Wehner and Andreas Winter. Entropic uncertainty relations—a survey. New Journal of Physics, 12 (2): 025009, feb 2010. 10.1088/​1367-2630/​12/​2/​025009.

[9] Patrick J. Coles, Mario Berta, Marco Tomamichel, and Stephanie Wehner. Entropic uncertainty relations and their applications. Rev. Mod. Phys., 89: 015002, Feb 2017. 10.1103/​RevModPhys.89.015002.

[10] Seth Lloyd. Quantum enigma machines. arXiv preprint arXiv:1307.0380, 2013.

[11] Andreas Winter. Weak locking capacity of quantum channels can be much larger than private capacity. Journal of Cryptology, 30 (1): 1–21, Jan 2017. ISSN 1432-1378. 10.1007/​s00145-015-9215-3.

[12] Cosmo Lupo and Seth Lloyd. Quantum data locking for high-rate private communication. New Journal of Physics, 17 (3): 033022, 2015. 10.1088/​1367-2630/​17/​3/​033022.

[13] Daniel J. Lum, John C. Howell, M. S. Allman, Thomas Gerrits, Varun B. Verma, Sae Woo Nam, Cosmo Lupo, and Seth Lloyd. Quantum enigma machine: Experimentally demonstrating quantum data locking. Phys. Rev. A, 94: 022315, Aug 2016. 10.1103/​PhysRevA.94.022315.

[14] Yang Liu, Zhu Cao, Cheng Wu, Daiji Fukuda, Lixing You, Jiaqiang Zhong, Takayuki Numata, Sijing Chen, Weijun Zhang, Sheng-Cai Shi, Chao-Yang Lu, Zhen Wang, Xiongfeng Ma, Jingyun Fan, Qiang Zhang, and Jian-Wei Pan. Experimental quantum data locking. Phys. Rev. A, 94: 020301, Aug 2016. 10.1103/​PhysRevA.94.020301.

[15] Jelena Notaros, Jacob Mower, Mikkel Heuck, Cosmo Lupo, Nicholas C. Harris, Gregory R. Steinbrecher, Darius Bunandar, Tom Baehr-Jones, Michael Hochberg, Seth Lloyd, and Dirk Englund. Programmable dispersion on a photonic integrated circuit for classical and quantum applications. Opt. Express, 25 (18): 21275–21285, Sep 2017. 10.1364/​OE.25.021275.

[16] Daniele Cozzolino, Beatrice Da Lio, Davide Bacco, and Leif Katsuo Oxenløwe. High-dimensional quantum communication: Benefits, progress, and future challenges. Advanced Quantum Technologies, 2 (12): 1900038, 2019. 10.1002/​qute.201900038.

[17] Yu He, X. Ding, Z.-E. Su, H.-L. Huang, J. Qin, C. Wang, S. Unsleber, C. Chen, H. Wang, Y.-M. He, X.-L. Wang, W.-J. Zhang, S.-J. Chen, C. Schneider, M. Kamp, L.-X. You, Z. Wang, S. Höfling, Chao-Yang Lu, and Jian-Wei Pan. Time-bin-encoded boson sampling with a single-photon device. Phys. Rev. Lett., 118: 190501, May 2017. 10.1103/​PhysRevLett.118.190501.

[18] Han-Sen Zhong, Yuan Li, Wei Li, Li-Chao Peng, Zu-En Su, Yi Hu, Yu-Ming He, Xing Ding, Weijun Zhang, Hao Li, Lu Zhang, Zhen Wang, Lixing You, Xi-Lin Wang, Xiao Jiang, Li Li, Yu-Ao Chen, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan. 12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion. Phys. Rev. Lett., 121: 250505, Dec 2018. 10.1103/​PhysRevLett.121.250505.

[19] Hui Wang, Jian Qin, Xing Ding, Ming-Cheng Chen, Si Chen, Xiang You, Yu-Ming He, Xiao Jiang, L. You, Z. Wang, C. Schneider, Jelmer J. Renema, Sven Höfling, Chao-Yang Lu, and Jian-Wei Pan. Boson sampling with 20 input photons and a 60-mode interferometer in a $1{0}^{14}$-dimensional hilbert space. Phys. Rev. Lett., 123: 250503, Dec 2019a. 10.1103/​PhysRevLett.123.250503.

[20] Paolo Aniello, Cosmo Lupo, and Mario Napolitano. Exploring representation theory of unitary groups via linear optical passive devices. Open Sys. & Inf. Dynamics, 13: 415, 2006. 10.1007/​s11080-006-9023-1.

[21] Frédéric Dupuis, Jan Florjanczyk, Patrick Hayden, and Debbie Leung. The locking-decoding frontier for generic dynamics. Proc. R. Soc. A, 469: 2159, 2013. 10.1098/​rspa.2013.0289.

[22] Huang Zixin, Pieter Kok, and Cosmo Lupo. Protecting the output of a quantum computer with random circuit samplers. arXiv:2003.11470, 2020.

[23] Mark M Wilde. Quantum information theory. Cambridge University Press, 2013.

[24] C. H. Bennett, G. Brassard, and J.-M. Robert. Privacy amplification by public discussion. SIAM J. Comput., 17: 210, 1988.

[25] Radosław Adamczak. Metric and classical fidelity uncertainty relations for random unitary matrices. Journal of Physics A: Mathematical and Theoretical, 50 (10): 105302, feb 2017. 10.1088/​1751-8121/​aa5662.

[26] Michael Reck, Anton Zeilinger, Herbert J. Bernstein, and Philip Bertani. Experimental realization of any discrete unitary operator. Phys. Rev. Lett., 73 (1): 58–61, July 1994. 10.1103/​PhysRevLett.73.58.

[27] William R. Clements, Peter C. Humphreys, Benjamin J. Metcalf, W. Steven Kolthammer, and Ian A. Walmsley. Optimal design for universal multiport interferometers. Optica, 3 (12): 1460–1465, Dec 2016. 10.1364/​OPTICA.3.001460.

[28] Cosmo Lupo, Mark M. Wilde, and Seth Lloyd. Robust quantum data locking from phase modulation. Phys. Rev. A, 90: 022326, Aug 2014. 10.1103/​PhysRevA.90.022326.

[29] P. D. Drummond, B. Opanchuk, L. Rosales-Zárate, M. D. Reid, and P. J. Forrester. Scaling of boson sampling experiments. Phys. Rev. A, 94: 042339, Oct 2016. 10.1103/​PhysRevA.94.042339.

[30] Rudolf Ahlswede and Andreas Winter. Strong converse for identification via quantum channels. IEEE Transactions on Information Theory, 48 (3): 569–579, 2002. 10.1109/​18.985947.

[31] Andreas Maurer. A bound on the deviation probability for sums of non-negative random variables. J. Inequalities in Pure and Applied Mathematics, 4 (1): 15, 2003.

[32] Hui Wang, Jian Qin, Xing Ding, Ming-Cheng Chen, Si Chen, Xiang You, Yu-Ming He, Xiao Jiang, L. You, Z. Wang, C. Schneider, Jelmer J. Renema, Sven Höfling, Chao-Yang Lu, and Jian-Wei Pan. Boson sampling with 20 input photons and a 60-mode interferometer in a $1{0}^{14}$-dimensional Hilbert space. Phys. Rev. Lett., 123: 250503, Dec 2019b. 10.1103/​PhysRevLett.123.250503.

[33] Scott Aaronson and Alex Arkhipov. The computational complexity of linear optics. In Proceedings of the forty-third annual ACM symposium on Theory of computing, pages 333–342. ACM, 2011. 10.1145/​1993636.1993682.

[34] Scott Aaronson and Alex Arkhipov. Boson Sampling is far from uniform. Quantum Information & Computation, 14 (15-16): 1383–1423, 2014. http:/​/​arXiv:1309.7460.

[35] Stefan Scheel. Permanents in linear optical networks. https:/​/​​abs/​quant-ph/​0406127, 2004.

Cited by

[1] Cosmo Lupo, James T. Peat, Erika Andersson, and Pieter Kok, "Error-tolerant oblivious transfer in the noisy-storage model", Physical Review Research 5 3, 033163 (2023).

[2] Fang-Fang Du, Gang Fan, and Xue-Mei Ren, "Kerr-effect-based quantum logical gates in decoherence-free subspace", Quantum 8, 1342 (2024).

[3] Zixin Huang, Pieter Kok, and Cosmo Lupo, "Fault-tolerant quantum data locking", Physical Review A 103 5, 052611 (2021).

[4] Jinjing Shi, Yongze Tang, Yuhu Lu, Yanyan Feng, Ronghua Shi, and Shichao Zhang, "Quantum Circuit Learning with Parameterized Boson Sampling", IEEE Transactions on Knowledge and Data Engineering 1 (2021).

[5] Peyman Najafi, Pedro C. S. Costa, and Dominic W. Berry, "Optimum phase estimation with two control qubits", AVS Quantum Science 5 2, 023802 (2023).

[6] Dominik Hangleiter and Jens Eisert, "Computational advantage of quantum random sampling", Reviews of Modern Physics 95 3, 035001 (2023).

[7] Jinjing Shi, Yuhu Lu, Yanyan Feng, Duan Huang, Xiaoping Lou, Qin Li, and Ronghua Shi, "A quantum hash function with grouped coarse-grained boson sampling", Quantum Information Processing 21 2, 73 (2022).

[8] Yanyan Feng, Ronghua Shi, Jinjing Shi, Wei Zhao, Yuhu Lu, and Yongze Tang, "Arbitrated quantum signature protocol with boson sampling-based random unitary encryption", Journal of Physics A Mathematical General 53 13, 135301 (2020).

[9] Dominik Hangleiter, "Sampling and the complexity of nature", arXiv:2012.07905, (2020).

[10] Raphael A. Abrahao, Arman Mansouri, and Austin P. Lund, "Boson Sampling with Gaussian input states: efficient scaling and certification", arXiv:1812.08978, (2018).

[11] Juan Carlos Garcia-Escartin, "Physical Unclonable Functions with Boson Sampling", arXiv:1911.08417, (2019).

The above citations are from Crossref's cited-by service (last updated successfully 2024-07-16 02:55:31) and SAO/NASA ADS (last updated successfully 2024-07-16 02:55:32). The list may be incomplete as not all publishers provide suitable and complete citation data.