Mateus Araújo

The degree of experimentally attainable nonlocality, as gauged by the loophole-free or effective violation of Bell inequalities, remains severely limited due to inefficient detectors. We address an experimentally motivated question: Which quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors? For any Bell inequality and any specification of detection efficiencies, the optimal strategies are those that maximally violate a tilted version of the Bell inequality in ideal conditions. In the simplest scenario, we demonstrate that the quantum strategies that maximally violate the doubly-tilted versions of Clauser-Horne-Shimony-Holt inequality are unique up to local isometries. We utilize Jordan's lemma and Grobner basis-based proof technique to analytically derive self-testing statements for the entire family of doubly-tilted CHSH inequalities and numerically demonstrate their robustness. These results enable us to reveal the insufficiency of even high levels of the Navascues-Pironio-Acin hierarchy to saturate the maximum quantum violation of these inequalities.

When transforming pairs of independent quantum operations according to the fundamental rules of quantum theory, an intriguing phenomenon emerges: some such higher-order operations may act on the input operations in an indefinite causal order. Recently, the formalism of process matrices has been developed to investigate these noncausal properties of higher-order operations. This formalism predicts, in principle, statistics that ensure indefinite causal order even in a device-independent scenario, where the involved operations are not characterised. Nevertheless, all physical implementations of process matrices proposed so far require full characterisation of the involved operations in order to certify such phenomena. Here we consider a semi-device-independent scenario, which does not require all operations to be characterised. We introduce a framework for certifying noncausal properties of process matrices in this intermediate regime and use it to analyse the quantum switch, a well-known higher-order operation, to show that, although it can only lead to causal statistics in a device-independent scenario, it can exhibit noncausal properties in semi-device-independent scenarios. This proves that the quantum switch generates stronger noncausal correlations than it was previously known.

Numerical security proofs based on conic optimization are known to deliver optimal secret-key rates, but so far they have mostly assumed that the emitted states are fully characterized. In practice, this assumption is unrealistic, since real devices inevitably suffer from imperfections and side channels that are extremely difficult to model in detail. Here, we extend conic-optimization methods to scenarios where only partial information about the emitted states is known, covering both prepare-and-measure and measurement-device-independent protocols. We demonstrate that our method outperforms state-of-the-art analytical and numerical approaches under realistic source imperfections, especially for protocols that use non-qubit encodings. These results advance numerical-based proofs towards a standard, implementation-ready framework for evaluating quantum key distribution protocols in the presence of source imperfections.

Finite-size general security proofs for quantum key distribution based on Rényi entropies have recently been introduced. These approaches are more flexible and provide tighter bounds on the secret key rate than traditional formulations based on the von Neumann entropy. However, deploying them requires minimizing the conditional Rényi entropy, a difficult optimization problem that has hitherto been tackled using ad-hoc techniques based on the Frank-Wolfe algorithm, which are unstable and can only handle particular cases. In this work, we introduce a method based on non-symmetric conic optimization for solving this problem. Our technique is fast, reliable, and completely general. We illustrate its performance on several protocols, whose results represent an improvement over the state of the art.

Finite-size general security proofs for QKD based on Rényi entropies offer more flexible and provide tighter bounds on the secret key rate than traditional formulations based on the von Neumann entropy. However, deploying them requires minimizing the conditional Rényi entropy, a difficult optimization problem that has commonly been tackled using ad-hoc techniques based on the Frank-Wolfe algorithm, which are unstable and can only handle particular cases. In this work, we introduce a method based on non-symmetric conic optimization for solving this problem. Our technique is fast, reliable, and completely general. We illustrate its performance on several protocols, whose results represent an improvement over the state of the art.

Computing key rates in QKD numerically is essential to unlock more powerful protocols, that uses more sophisticated measurement bases or quantum systems of higher dimension. It is a difficult optimization problem, that depends on minimizing a convex non-linear function, the relative entropy. The gold standard for solving such problems is a primal-dual interior-point algorithm, that is highly efficient and inherently gives upper and lower bounds. Recently one such algorithm was discovered for non-symmetric cones, a category that includes the relative entropy, and was previously out of reach.

Continuous variable quantum key distribution (CVQKD) with discrete modulation combines advantages of CVQKD, such as the implementability using readily available technologies, with advantages of discrete variable quantum key distribution, such as easier error correction procedures. In this work we consider a phase-shift keying protocol using four coherent states (4-PSK protocol) and coarse-grained heterodyne measurements. We provide a security proof against coherent attacks and compute the achievable key rate in a finite size setting, i.e. with a finite number of rounds. To this end, we employ the generalized entropy accumulation theorem, as well conic optimisation, providing us with improved key rates compared to previous works. At metropolitan distances our method can provide positive key rates for the order of $10^9$ rounds. We also provide a theoretical method to overcome the assumption of a finite photon number cutoff made in previous works.