Wiesner's unforgeable quantum money scheme is widely celebrated as the first quantum information application. Based on the nocloning 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.

Quantum cryptography harnesses quantum light, in particular single photons, to provide security guarantees that cannot be reached by classical means. For each cryptographic task, the security feature of interest is directly related to the photons’ non-classical properties. Quantum dot-based single-photon sources are remarkable candidates, as they can in principle emit deterministically, with high brightness and low multiphoton contribution. Here, we show that these sources provide additional security benefits, thanks to the tunability of coherence in the emitted photon-number states. We identify the optimal optical pumping scheme for the main quantum-cryptographic primitives, and benchmark their performance with respect to Poisson-distributed sources such as attenuated laser states and down-conversion sources. In particular, we elaborate on the advantage of using phonon-assisted and two-photon excitation rather than resonant excitation for quantum key distribution and other primitives. The presented results will guide future developments in solid-state and quantum information science for photon sources that are tailored to quantum communication tasks.

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.In contrast to classical physics, quantum mechanical systems have a no-cloning property [1]: it is impossible to make a perfect copy of a quantum object in an unknown state. This property was used by Wiesner in his proposal to mint unforgeable quantum money [2], giving birth to the field of quantum cryptography [3][4][5]. The original idea involved a bank encoding a secret classical key into a sequence of two-level quantum states (qubits) stored in a quantum memory and handed to a client. The secret key specifies the basis in which each qubit is encoded, ensuring that a forger ignoring the basis in which to measure it will destroy information. This will then trigger incorrect measurement outcomes when the bank will verify the validity of the banknote. Such a scheme may be impractical over long distances due to a potentially lossy and noisy transmission of the quantum states between the client and the bank. It was also shown to be vulnerable to adaptive attacks, where a counterfeiter can use the same banknote several times [6]. An alternative protocol with verification using classical communication was first proposed in [7] and extended to practical, noise-tolerant schemes in [8][9][10].Although quantum key distribution protocols have been widely studied and implemented [11], quantum money has not yet seen the same experimental progress, essentially because of the difficulty in implementing efficient quantum storage devices [12]. However, the experimental interest in quantum money has grown recently, with demonstration of forgery of quantum banknotes [13] and implementation of weak coherent state-based quantum credit card schemes, secure in a trusted terminal scenario [14,15], in the prospect of near-future implementations with a quantum memory. These require new security proofs tackling the optimal cloning of coherent states, differing from qubit-based quantum money and also quantum key distribution proofs.In quantum cryptography, semi-device-independent frameworks have been developed in order to limit the needed assumptions to ensure secur...