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Quantum superiority with coherent states

Periodic Reporting for period 2 - QUSCO (Quantum superiority with coherent states)

Reporting period: 2019-07-01 to 2020-12-31

Quantum technologies explore the possibility of harnessing the power of quantum properties of physical systems to demonstrate in practice an advantage in terms of computational time, security or communication efficiency. Such an advantage can revolutionize current practices in information processing and communication, with a range of applications in financial, government and medical transactions, critical infrastructure protection, material design, network management, and many more. The deployment however of a large-scale quantum network connecting devices such as quantum computers or sensors that would be able to unlock the full potential of quantum resources may lie several years or even decades ahead. While we advance in this direction, it is crucial to demonstrate that current and near-term quantum technologies can already be exploited for enabling or enhancing useful tasks in a way that cannot be achieved by classical means.

In QUSCO, we pursue this objective using photonic systems, where information is typically encoded in properties of single or entangled photons. The photonic experimental platform is perfectly suited for communication of quantum information thanks to the inherent robustness of photons to losses during propagation. It can also be used currently for performing small-scale quantum computations and additionally provides a promising path to integration, which can drastically enhance the scalability of the resulting systems. Based on this technology and on a strong interaction between experimental physics and theoretical computer science, we conceive and implement advanced communication and computation protocols exhibiting a provable quantum advantage.
Although the ability to share unconditionally secret messages, enabled by Quantum Key Distribution (QKD), is arguably one of the most emblematic applications of quantum technologies, there is a wide range of functionalities where quantum resources can be used to surpass the performance of classical systems. The major challenge here is to adapt protocols to real-world conditions and demonstrate a provable gap between classical and quantum information in practical communication scenarios.

An important functionality that we examined in QUSCO was performing transactions with unforgeable quantum money. Unforgeable quantum money was historically the first application of quantum information and dates back to Wiesner in 1977. Until recently, however, the lack of realistic protocols and of robust and practical storage and detection devices has prohibited its implementation. In high level, the idea is to use the no-cloning property of quantum mechanics to authenticate and perform credit card-based transactions with maximal security guarantees (the same idea was in fact shortly afterwards used to propose the much celebrated BB84 QKD protocol). We first performed the security analysis in a realistic setting of a scheme that was devised to rely solely on polarization-encoded single-photon state generation and measurement, as well as classical verification techniques. This enabled a proof-of-principle implementation with an on-the-fly credit card in a fibre-optic setup, where we satisfied the unforgeability criterion within the system operation regime. We have completed this work with a general security framework for quantum money schemes using weak coherent states simulating true single photons, as is typically done in practical implementations including our experiment, and anticipating for the use of a quantum memory storing the quantum money states.

The next protocol we considered, which is at the heart of QUSCO, belongs to the field of communication complexity, which studies how much communication is necessary to solve a distributed task. It has wide-range applications, including, for instance, for the optimization of very large-scale integrated circuits and data structures. In quantum networks, the execution of such protocols requires a party to generate and locally manipulate a large entangled state, before sending it to a second party who checks the solution of the problem. A fundamental primitive to achieve such tasks is Hidden Matching, which enables two parties to perform data equality checks. Quantum Hidden Matching has been shown to be superior to its counterpart and relies on the use of specific states known as quantum fingerprints. In QUSCO, we used a previously proposed and very interesting from a practical point of view method for implementing these states using superpositions of coherent states over multiple time modes, followed by manipulation with linear optics and then single-photon detection. This coherent state mapping technique enabled us to perform an experiment rigorously demonstrating an advantage in the amount of transmitted information for solving a simplified version of Hidden Matching that we called Sampling Matching. Our experiment involves an innovative passive technique and the main challenges it faced were the stringent conditions in terms of the interferometric visibility and the dark counts of the single-photon detectors that were required to demonstrate the desired advantage. As with all quantum protocol implementations, it was also necessary to carefully assess our results with respect to classical protocols using equivalent resources, with the ultimate goal of rigorously demonstrating a reduction of communication complexity using practical photonic devices.

In addition to proving that quantum is indeed superior to classical communication for useful tasks, the above experiment was also the first step on the path of the goal of demonstrating a quantum computational advantage for the verification of computationally hard (NP) problems. This is the core of QUSCO. We first laid down the theoretical construction for addressing this verification task with linear optics, and then adapted it to the coherent state mapping that was used in the aforementioned quantum communication complexity experiment. This crucial step enabled us to overcome important scalability issues that were inherent in the initial proposal, and to demonstrate experimentally the targeted quantum computational advantage, for the first time in such an interactive communication scenario. In parallel, we have further highlighted the power of linear optics in quantum information with theoretical work that examined this platform for performing optimal quantum-programmable projective measurements.
The experimental demonstrations achieved in QUSCO have all been the first to show a quantum advantage for the tasks under study, and include a rigorous theoretical analysis and realistic implementation conditions. Importantly, they span an enhancement in performance in security (quantum money), communication efficiency (Sampling Matching) and computational time (NP verification), and hence enrich substantially the available application toolbox of quantum technologies for the emerging quantum networks.

Our focus in the second half of the project will be to perform the quantum money including storage and to use our coherent state experimental platform, enhanced with high-performance nanowire superconducting detectors, for the demonstration of tasks such as the estimation of the Euclidean distance between data strings, which is useful for instance in machine learning. We will also exploit an entangled-photon experimental platform for exploring further applications tailored to quantum networks.
Illustration by Kevin Hong (Quanta magazine) for our quantum communication complexity experiment.