Quantum cryptography integrating an optical quantum memory

TL;DR

This work demonstrates, for the first time, a cryptographic primitive that integrates an optical quantum memory by implementing Wiesner's unforgeable quantum money with an intermediate memory layer. A high-efficiency cold-atom memory stores polarization qubits encoded as weak coherent states, enabling on-demand retrieval and verification by a vendor; the experiment shows memory efficiency around $\eta=(77\pm2)\%$ with low error rates, placing the operation in a provably secure regime for suitable $\mu$ values. The security analysis combines phase-randomized weak coherent-state modelling, semidefinite programming, and the Choi–Jamiolkowski framework to derive practical thresholds for memory-assisted quantum money. The results establish memory-enabled quantum cryptographic functionality, with implications for memory-assisted networks, two-way protocols, and secure distributed quantum technologies.

Abstract

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 first 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 new avenues for quantum memory utilization and network functionalities.

Figures (5)

• Figure 1: Quantum cryptographic protocol with an intermediate quantum memory layer. In future quantum networks and use cases as unforgeable quantum money, optical memories, which allow data to be stored and retrieved on demand, play a central role. The incorporation of these memories puts stringent constraints on secure operation regions in terms of storage-and-retrieval efficiency and added noise.
• Figure 2: Quantum money protocol with memory storage and retrieval. (A) The bank encodes a random secret key into a sequence of polarisation qubits chosen from two bases, $\{\ket{H},\ket{V}\}$ or $\{\ket{\sigma^+},\ket{\sigma^-}\}$, and stores them into a quantum memory provided to the client. In a transaction, the client retrieves the states from the memory and hands them to the vendor who performs the measurement in one of the encoding bases. For verification, the vendor communicates the measurement results and the chosen basis to the bank, allowing to calculate the error rate $\varepsilon$. (B) The communication is considered secure if the error rate falls below a specified threshold (solid lines), which is highly dependent on the mean photon-number per pulse $\mu$ for weak coherent states and on the memory efficiency $\eta$. (C) For a typical mean photon-number per pulse $\mu=1$, a successful protocol (shaded area) requires high efficiency and low error rate. The blue point indicates our experimental result.
• Figure 3: Experimental setup. The three panels illustrate the encoding process (bank), the transmission line incorporating a quantum memory (client), and the detection stage (vendor). A quantum random number generator (QRNG) generates a secret key, which is used after voltage conversion (DAC) and amplification to prepare polarization states encoded on weak coherent states via a Pockels cell. The qubit states are then stored in a quantum memory based on an elongated ensemble of laser-cooled cesium atoms with ultra-high optical depth. An additional laser field dynamically controls the reversible mapping. To optimize storage, the polarization qubits are first converted into dual-rail qubits using a beam displacer (BD), and the reverse process is performed after retrieval. At the final stage, the polarisation states are measured in a chosen $\bigl\{H,V\bigr\}$ or $\bigl\{\sigma^+,\sigma^-\bigr\}$ basis using waveplates (QW, HW), a polarizing beam splitter (PBS), and two single-photon avalanche photodiodes (APD). Fabry-Perot cavities (FPC) are employed to filter the residual control beam leakage. The error rate $\varepsilon$ is determined by comparing the acquired data to the secret key through a classical channel.
• Figure 4: Experimental results and security threshold. The error rates are shown for different mean photon numbers per pulse $\mu$, without storage indicated in grey and with intermediate storage in blue. These rates are calculated as the average of error rates for the two measurement bases. The light red area represents the security threshold determined for a measured average efficiency of $\eta=(77\pm2)\%$ across the four mean photon numbers. Error bars for the error rates account for the statistical uncertainty of photon counts while error bars on the mean photon numbers correspond to power fluctuations during the overall data acquisition.
• Figure S1: Timing diagram of the experiment. A very elongated MOT is first loaded, followed by a compression and a polarization gradient cooling (PGC) stage. Then, during a 2-ms phase, the atomic ensemble is used for the cryptographic protocol implementation, with successive storage and retrieval of the optical qubits.