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

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Abstract

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.

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

[3] 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).

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

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

[6] 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).

[7] 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).

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

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

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