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Experimental demonstration of practical unforgeable quantum money

Mathieu Bozzio, Adeline Orieux, Luis Trigo Vidarte, Isabelle Zaquine, Iordanis Kerenidis, Eleni Diamanti

Published Sep 18, 2017• 1 citation
OpenAlex

Abstract

Wiesner's unforgeable quantum money scheme is widely celebrated as the first quantum information application. Based on the no-cloning property of quantum mechanics, this scheme allows for the creation of credit cards used in authenticated transactions offering security guarantees impossible to achieve by classical means. However, despite its central role in quantum cryptography, its experimental implementation has remained elusive because of the lack of realistic protocols adapted to practical quantum storage devices and verification techniques. Here, we experimentally demonstrate a quantum money protocol that rigorously satisfies the security condition for unforgeability, using a practical system exploiting single-photon polarization encoding of highly attenuated coherent states of light for on-the-fly credit card state generation and readout. Our implementation includes classical verification and is designed to be compatible with state-of-the-art quantum memories, which have been taken into account in the security analysis, together with all system imperfections. Our results constitute a major step towards a real-world realization of this milestone protocol.

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Wiesner's unforgeable quantum money scheme is widely celebrated as the first quantum information application. Based on the no-cloning property of quantum mechanics, this scheme allows for the creation of credit cards used in authenticated transactions offering security guarantees impossible to achieve by classical means. However, despite its central role in quantum cryptography, its experimental implementation has remained elusive because of the lack of realistic protocols adapted to practical quantum storage devices and verification techniques. Here, we experimentally demonstrate a quantum money protocol that rigorously satisfies the security condition for unforgeability, using a practical system exploiting single-photon polarization encoding of highly attenuated coherent states of light for on-the-fly credit card state generation and readout. Our implementation includes classical verification and is designed to be compatible with state-of-the-art quantum memories, which have been taken into account in the security analysis, together with all system imperfections. Our results constitute a major step towards a real-world realization of this milestone protocol.
Abstract Wiesner’s unforgeable quantum money scheme is widely celebrated as the first quantum information application. Based on the no-cloning property of quantum mechanics, this scheme allows for the creation of credit cards used in authenticated transactions offering security guarantees impossible to achieve by classical means. However, despite its central role in quantum cryptography, its experimental implementation has remained elusive because of the lack of quantum memories and of practical verification techniques. Here, we experimentally implement a quantum money protocol relying on classical verification that rigorously satisfies the security condition for unforgeability. Our system exploits polarization encoding of weak coherent states of light and operates under conditions that ensure compatibility with state-of-the-art quantum memories. We derive working regimes for our system using a security analysis taking into account all practical imperfections. Our results constitute a major step towards a real-world realization of this milestone protocol.
The no-cloning property of quantum mechanics allows unforgeability of quantum banknotes and credit cards. Quantum credit card protocols involve a bank, a client, and a payment terminal and their practical implementation typically relies on encoding information on weak coherent states of light. Here, we provide a security proof in this practical setting for semi-device-independent quantum money with classical verification, involving an honest bank, a dishonest client, and a potentially untrusted terminal. Our analysis uses semidefinite programming in the coherent state framework and aims at simultaneously optimizing over the noise and losses introduced by a dishonest party. We discuss secure regimes of operation in both fixed and randomized phase settings, taking into account experimental imperfections. Finally, we study the evolution of protocol security in the presence of a decohering optical quantum memory and identify secure credit card lifetimes for a specific configuration.
Developments in scalable quantum networks rely critically on optical quantum memories, which are key components enabling the storage of quantum information. These memories play a pivotal role for entanglement distribution and long-distance quantum communication, with remarkable advances achieved in this context. However, optical memories have broader applications, and their storage and buffering capabilities can benefit a wide range of future quantum technologies. Here, we present the demonstration of a cryptography protocol incorporating an intermediate quantum memory layer. Specifically, we implement Wiesner's unforgeable quantum money primitive with a storage step, rather than as an on-the-fly procedure. This protocol imposes stringent requirements on storage efficiency and noise level to reach a secure regime. We demonstrate the implementation with polarization encoding of weak coherent states of light and a high-efficiency cold atom-based quantum memory and validate the full scheme. Our results showcase a major capability, opening broader avenues for quantum memory utilization and network functionalities.
Harnessing the laws of quantum theory can drastically boost the security of modern communication networks, from public key encryption to electronic voting and online banking. In this thesis, we bridge the gap between theory and experiment regarding two quantum-cryptographic tasks: quantum money and quantum weak coin flipping. Quantum money exploits the no-cloning property of quantum physics to generate unforgeable tokens, banknotes, and credit cards. We provide the first proof-of-principle implementation of this task, using photonic systems at telecom wavelengths. We then develop a practical security proof for quantum credit card schemes, in which the bank can remotely verify a card even in the presence of a malicious payment terminal. We finally propose a setup for secure quantum storage of the credit card, using electromagnetically-induced transparency in a cloud of cold cesium atoms. Quantum weak coin flipping is a fundamental cryptographic primitive, which helps construct more complex tasks such as bit commitment and multiparty computation. It allows two distant parties to flip a coin when they both desire opposite outcomes. Using quantum entanglement then prevents any party from biasing the outcome of the flip beyond a certain probability. We propose the first implementation for quantum weak coin flipping, which requires a single photon and linear optics only. We provide the complete security analysis in the presence of noise and losses, and show that the protocol is implementable on the scale of a small city with current technology. We finally propose a linear-optical extension of the protocol to lower the coin bias.
The realization of devices that harness the laws of quantum mechanics represents an exciting challenge at the interface of modern technology and fundamental science. An exemplary paragon of the power of such quantum primitives is the concept of “quantum money” [Wiesner S (1983) ACM SIGACT News 15:78–88]. A dishonest holder of a quantum bank note will invariably fail in any counterfeiting attempts; indeed, under assumptions of ideal measurements and decoherence-free memories such security is guaranteed by the no-cloning theorem. In any practical situation, however, noise, decoherence, and operational imperfections abound. Thus, the development of secure “quantum money”-type primitives capable of tolerating realistic infidelities is of both practical and fundamental importance. Here, we propose a novel class of such protocols and demonstrate their tolerance to noise; moreover, we prove their rigorous security by determining tight fidelity thresholds. Our proposed protocols require only the ability to prepare, store, and measure single quantum bit memories, making their experimental realization accessible with current technologies.
Abstract Unknown quantum information cannot be perfectly copied (cloned). This statement is the bedrock of quantum technologies and quantum cryptography, including the seminal scheme of Wiesner’s quantum money, which was the first quantum-cryptographic proposal. Surprisingly, to our knowledge, quantum money has not been tested experimentally yet. Here, we experimentally revisit the Wiesner idea, assuming a banknote to be an image encoded in the polarization states of single photons. We demonstrate that it is possible to use quantum states to prepare a banknote that cannot be ideally copied without making the owner aware of only unauthorized actions. We provide the security conditions for quantum money by investigating the physically-achievable limits on the fidelity of 1-to-2 copying of arbitrary sequences of qubits. These results can be applied as a security measure in quantum digital right management.