Experimental preparation and verification of quantum money

Jian-Yu Guan, Juan Miguel Arrazola, Ryan Amiri, Weijun Zhang, Hao Li, Lixing You, Zhen Wang, Qiang Zhang, and Jian-Wei Pan

Phys. Rev. A 97, 032338 – Published 27 March 2018

Abstract

A quantum money scheme enables a trusted bank to provide untrusted users with verifiable quantum banknotes that cannot be forged. In this work, we report a proof-of-principle experimental demonstration of the preparation and verification of unforgeable quantum banknotes. We employ a security analysis that takes experimental imperfections fully into account. We measure a total of $3.6 \times 10^{6}$ states in one verification round, limiting the forging probability to $10^{- 7}$ based on the security analysis. Our results demonstrate the feasibility of preparing and verifying quantum banknotes using currently available experimental techniques.

Received 21 September 2017

DOI:https://doi.org/10.1103/PhysRevA.97.032338

Physics Subject Headings (PhySH)

Quantum communication Quantum cryptography Quantum optics

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Jian-Yu Guan^1,2, Juan Miguel Arrazola³, Ryan Amiri⁴, Weijun Zhang⁵, Hao Li⁵, Lixing You⁵, Zhen Wang⁵, Qiang Zhang^1,2, and Jian-Wei Pan^1,2

¹Shanghai Branch, Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
²CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, Shanghai Branch, University of Science and Technology of China, Hefei, Anhui 230026, China
³Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
⁴SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
⁵State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, P. R. China

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Vol. 97, Iss. 3 — March 2018

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Images

Figure 1
Schematic illustration of the quantum money protocol. The bank produces $N$ quantum states $|x^{1}〉, |x^{2}〉, ..., |x^{N}〉$ according to a random secret string $x = x^{1} x^{2} \dots x^{N}$ . The bank also assigns a unique serial number to the banknote and creates a register $r$ that records whether each state has been used previously for verification. To verify the banknote, a holder randomly selects $l$ quantum states. For each state, the holder randomly selects one of the three matchings $M_{1}, M_{2}, M_{3}$ and performs the corresponding measurement. The outcomes consist of a matching pair $(i, j)$ and a parity bit $b$ , which are recorded and sent for comparison with the bank's secret string $x$ . The banknote is accepted as valid if the error rate observed by the bank is sufficiently low.
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Figure 2
(a) Experimental setup for generating and verifying quantum banknotes. A laser source produces sequences of coherent states which are modulated in phase according to a secret string $x$ and attenuated to an amplitude of ${| α |}^{2} = 0.25$ . The signals are passively split into three arms using a $1 \times 3$ beam-splitter and routed to three Mach-Zehnder interferometers. The interferometers, which, respectively, have delays of 2, 4, and 6 ns, are standard fiber Michelson interferometers. Each of them consists of a single beam-splitter and two Faraday mirrors. The delays are depicted in the figure in terms of the varying length of the lower arm of the interferometer connected to the mirror. Delays of lengths 5 and 10 m are placed to distinguish the outputs of each interferometer, which are recombined using a $1 \times 3$ beam-splitter and measured using superconducting nanowire single-photon detectors. IM: Intensity Modulator. PM: Phase Modulator. ATT: Attenuator. BS: beam-splitter ( $2 \times 2$ and $1 \times 3$ ). Cir: Circulator. FM: Faraday Mirror. PC: Polarization Controller. (b) The block structure scheme. The graph in the left side shows the initial state, consisting of a total of four pulses. The graph in the right side shows the detection time-bins in one cycle, which consist of three parts corresponding to a 4, a 2, and a 6 ns MZI, respectively. The delay of the three parts are mainly decided by the length of delay lines.
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Figure 3
Experimental error rate for different values of the number of states $l$ used in the verification. The standard error is calculated from ten rounds of experiments. The red solid line shows $e_{min}$ , the minimum average error rate caused by an adversary, the magenta dashed line shows the acceptance threshold, and the shaded area corresponds to values of the error rate where the banknote is accepted. The genuine banknotes generated in the experiment can pass the verification, and coincide with the calibration results $β = 0.033$ .
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Figure 4
Forging probability for different values of the number of states used in verification $l$ . The blue line corresponds to our experimental parameters while the green line corresponds to the ideal case. The dashed line represents the $10^{- 7}$ target security level.
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Figure 5
The relationship between $e_{min}$ and $ε$ .
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Figure 6
Optimization curves for computing ${max}_{ε} min T_{2}, T_{3}$ .
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