arXiv subjects

Mateus Araújo

Publications and source records attributed to Mateus Araújo.

At least 19 recordsLinked to original sources

arXiv2026

Effective discrete-modulated continuous variable QKD under general attacks using dimension reduction

Continuous variable quantum key distribution via discrete modulations ensures information-theoretic security using standard telecom technologies, providing affordable and scalable quantum communications with simplified classical postprocessing. However, existing security proofs against general attacks often rely on restrictive assumptions, such as a bounded dimension for coherent states, or require impractically large block sizes. In this work, we develop a finite-size security analysis that removes these limitations while incorporating realistic experimental features. Our approach combines an optimization under infinite dimensions, a security proof against general attacks, a trusted detector model accounting for the receiver imperfections, and postselection strategies to reuse discarded measurement outcomes. We report positive key rates in the finite-size regime for relevant block sizes of the order of $10^7$. These results contribute to narrowing the gap between theoretical security proofs and practical implementations of discrete-modulated continuous variable quantum key distribution protocols.

quant-ph↗

arXiv2026

Non-commutative optimization problems with differential constraints

Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where those might be defined. Many of these problems are known to admit a complete hierarchy of semidefinite programming (SDP) relaxations. In this work, we consider a variant of NPO problems where a subset of the operator variables satisfies a system of ordinary differential equations. We prove that, under mild conditions of operator boundedness, for every such problem one can construct a standard NPO problem with the same solution. This allows us to define a complete hierarchy of SDPs to tackle the original differential problem. We apply this method to bound averages of local observables in quantum spin systems subject to a Hamiltonian evolution (i.e., a quench). We find that, even in the thermodynamic limit of infinitely many sites, low levels of the hierarchy provide very good approximations for reasonably long evolution times.

quant-ph↗

arXiv2026

Tighter Asymptotic Key Rates for Intensity-Correlated Decoy-State QKD via Nonlinear Programming

Decoy-state QKD with phase-randomized weak coherent pulses is typically analyzed assuming independent, precisely prepared intensities. Real sources, however, can exhibit correlated intensity drift across rounds, potentially leaking intensity information and breaking the standard decoy-state reduction to linear programs. Cauchy--Schwarz (CS) constraints can restore security by coupling $n$-photon yields across intensities, but they introduce nonlinear square-root constraints that are commonly handled via outer linearisation around channel-model-based reference points. We propose a reproducible alternative: first solve the full CS-constrained parameter-estimation problems using the interior-point nonlinear solver IPOPT, then use the resulting candidate solution as the linearisation point for the outer optimisation that certifies a valid lower bound on the asymptotic key rate. Simulations for both coarse-grained model-independent correlations and fine-grained truncated-Gaussian models show consistently tighter key-rate bounds than canonical reference points, and in some cases allow certifying optimality when both optimisation stages coincide.

quant-ph↗

arXiv2026

Finite-size quantum key distribution rates from Rényi entropies using conic optimization

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.

quant-ph↗

arXiv2026

First-order optimality conditions for non-commutative optimization problems

We consider the problem of optimizing the state average of a polynomial of non-commuting variables, over all states and operators satisfying a number of polynomial constraints, and over all Hilbert spaces where such states and operators are defined. Such non-commutative polynomial optimization (NPO) problems are routinely solved through hierarchies of semidefinite programming (SDP) relaxations. By formulating the general NPO problem in Lagrangian terms, we heuristically derive first-order optimality conditions via small variations in the problem variables. Although the derivation is not rigorous, it gives rise to two types of optimality conditions -- state and operator -- which are rigorously analyzed in the paper. Both types of conditions can be enforced through additional positive semidefinite constraints in the SDP hierarchies. State optimality conditions are shown to be satisfied by all NPO problems. For NPO problems with optimal solutions (such as, e.g., Archimedean ones) they allow enforcing a new type of constraints: namely, restricting the optimization over states to the set of common ground states of an arbitrary number of operators. Operator optimality conditions are the non-commutative analogs of the Karush--Kuhn--Tucker (KKT) conditions, which are known to hold in many classical optimization problems. In this regard, we prove that a weak form of operator optimality holds for all NPO problems; stronger versions require the problem constraints to satisfy some qualification criterion, just like in the classical case (e.g.: Mangasarian--Fromovitz constraint qualification). We test the power of the new optimality conditions by computing local properties of ground states of many-body spin systems and the maximum quantum violation of Bell inequalities.

quant-ph↗

arXiv2026

Post-selection games

In this paper, we introduce post-selection games, a generalization of nonlocal games where each round can be not only won or lost by the players, but also discarded by the referee. Such games naturally formalize possibilistic proofs of nonlocality, such as Hardy's paradox. We develop algorithms for computing the local and Tsirelson bounds of post-selection games. Furthermore, we show that they have an unbounded advantage in statistical power over traditional nonlocal games, making them ideally suited for analysing Bell tests with low detection efficiency.

quant-ph↗

arXiv2025

Optimal key rates for quantum key distribution with partial source characterization

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.

quant-ph↗

arXiv2025

Self-testing tilted strategies for maximal loophole-free nonlocality

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 a Jordan's lemma and Gröbner 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 Navascués--Pironio--Acín hierarchy to saturate the maximum quantum violation of these inequalities.

quant-ph↗

arXiv2025

Bell nonlocality with a single shot

In order to reject the local hidden variables hypothesis, the usefulness of a Bell inequality can be quantified by how small a p-value it will give for a physical experiment. Here we show that to obtain a small expected p-value it is sufficient to have a large gap between the local and Tsirelson bounds of the Bell inequality, when it is formulated as a nonlocal game. We develop an algorithm for transforming an arbitrary Bell inequality into an equivalent nonlocal game with the largest possible gap, and show its results for the CGLMP and $I_{nn22}$ inequalities. We present explicit examples of Bell inequalities with gap arbitrarily close to one, and show that this makes it possible to reject local hidden variables with arbitrarily small p-value in a single shot, without needing to collect statistics. We also develop an algorithm for calculating local bounds of general Bell inequalities which is significantly faster than the naïve approach, which may be of independent interest.

quant-ph↗

arXiv2025

Quantum computation with indefinite causal structures

One way to study the physical plausibility of closed timelike curves (CTCs) is to examine their computational power. This has been done for Deutschian CTCs (D-CTCs) and post-selection CTCs (P-CTCs), with the result that they allow for the efficient solution of problems in PSPACE and PP, respectively. Since these are extremely powerful complexity classes, which are not expected to be solvable in reality, this can be taken as evidence that these models for CTCs are pathological. This problem is closely related to the nonlinearity of this models, which also allows for example cloning quantum states, in the case of D-CTCs, or distinguishing non-orthogonal quantum states, in the case of P-CTCs. In contrast, the process matrix formalism allows one to model indefinite causal structures in a linear way, getting rid of these effects, and raising the possibility that its computational power is rather tame. In this paper we show that process matrices correspond to a linear particular case of P-CTCs, and therefore that its computational power is upperbounded by that of PP. We show, furthermore, a family of processes that can violate causal inequalities but nevertheless can be simulated by a causally ordered quantum circuit with only a constant overhead, showing that indefinite causality is not necessarily hard to simulate.

quant-ph↗

arXiv2025

Quantum key distribution rates from non-symmetric conic optimization

Computing key rates in quantum key distribution (QKD) numerically is essential to unlock more powerful protocols, that use 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 (quantum) relative entropy. Standard conic optimization techniques have for a long time been unable to handle the relative entropy cone, as it is a non-symmetric cone, and the standard algorithms can only handle symmetric ones. Recently, however, a practical algorithm has been discovered for optimizing over non-symmetric cones, including the relative entropy. Here we adapt this algorithm to the problem of computation of key rates, obtaining an efficient technique for lower bounding them. In comparison to previous techniques it has the advantages of flexibility, ease of use, and above all performance.

quant-ph↗

arXiv2025

Self-testing in prepare-and-measure scenarios and a robust version of Wigner's theorem

We consider communication scenarios where one party sends quantum states of known dimensionality $D$, prepared with an untrusted apparatus, to another, distant party, who probes them with uncharacterized measurement devices. We prove that, for any ensemble of reference pure quantum states, there exists one such prepare-and-measure scenario and a linear functional $W$ on its observed measurement probabilities, such that $W$ can only be maximized if the preparations coincide with the reference states, modulo a unitary or an anti-unitary transformation. In other words, prepare-and-measure scenarios allow one to "self-test" arbitrary ensembles of pure quantum states. Arbitrary extreme $D$-dimensional quantum measurements, or sets thereof, can be similarly self-tested. Our results rely on a robust generalization of Wigner's theorem, a well-known result in particle physics that characterizes physical symmetries.

quant-ph↗

arXiv2025

Improved finite-size key rates for discrete-modulated continuous variable quantum key distribution under coherent attacks

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. We consider a prepare-and-measure CVQKD protocol, where Alice chooses from a set of four coherent states and Bob performs a heterodyne measurement, the result of which is discretised in both key and test rounds. We provide a security proof against coherent attacks in the finite-size regime, and compute the achievable key rate. To this end, we employ the generalised entropy accumulation theorem, as well as recent advances in conic optimisation, yielding improved key rates compared to previous works. At metropolitan distances, our method can provide positive key rates for the order of $10^8$ rounds.

quant-ph↗

arXiv2024

Semidefinite programming relaxations for quantum correlations

Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science. Many otherwise intractable fundamental and applied problems can be successfully approached by means of relaxation to a semidefinite program. Here, we review such methodology in the context of quantum correlations. We discuss how the core idea of semidefinite relaxations can be adapted for a variety of research topics in quantum correlations, including nonlocality, quantum communication, quantum networks, entanglement, and quantum cryptography.

quant-ph↗

arXiv2024

Introducing Moment: A toolkit for semi-definite programming with moment matrices

Non-commutative polynomial optimization is a powerful technique with numerous applications in quantum nonlocality, quantum key distribution, causal inference, many-body physics, amongst others. The standard approach is to reduce such optimizations to a hierarchy of semi-definite programs, which can be solved numerically using well-understood interior-point methods. A key, but computationally costly, step is the formulation of moment matrices, whose size (and hence cost) grows exponentially with the depth of the hierarchy. It is therefore essential to have highly-optimized software to construct moment matrices. Here, we introduce Moment: a toolkit that produces moment matrix relaxations from the specification of a non-commutative optimization problem. In order to obtain the absolute best performance, Moment is written in C++, and for convenience of use provides an interface via MATLAB. We benchmark Moment's performance, and see that it can be up to four orders of magnitude faster than current software with similar functionality.

quant-ph↗

arXiv2024

High-dimensional quantum key distribution using a multi-plane light converter

High-dimensional quantum key distribution (QKD) offers higher information capacity and stronger resilience to noise compared to its binary counterpart. However, these advantages are often hindered by the difficulty of realizing the required high-dimensional measurements and transformations. Here, we implement a large-scale multi-plane light converter (MPLC) and program it as a high-dimensional mode sorter of spatial modes for QKD. Using the MPLC, we demonstrate five-dimensional QKD with six mutually unbiased bases and 25-dimensional QKD with two mutually unbiased bases in the same experimental setup. Furthermore, we propose a construction of pairs of mutually unbiased bases that are robust to experimental errors, with measurement complexity scaling only with the square root of the encoded dimension. This approach paves the way for QKD implementations in higher dimensions.

quant-ph↗

arXiv2023

Quantum key distribution rates from semidefinite programming

Computing the key rate in quantum key distribution (QKD) protocols is a long standing challenge. Analytical methods are limited to a handful of protocols with highly symmetric measurement bases. Numerical methods can handle arbitrary measurement bases, but either use the min-entropy, which gives a loose lower bound to the von Neumann entropy, or rely on cumbersome dedicated algorithms. Based on a recently discovered semidefinite programming (SDP) hierarchy converging to the conditional von Neumann entropy, used for computing the asymptotic key rates in the device independent case, we introduce an SDP hierarchy that converges to the asymptotic secret key rate in the case of characterised devices. The resulting algorithm is efficient, easy to implement and easy to use. We illustrate its performance by recovering known bounds on the key rate and extending high-dimensional QKD protocols to previously intractable cases. We also use it to reanalyse experimental data to demonstrate how higher key rates can be achieved when the full statistics are taken into account.

quant-ph↗

arXiv2023

Comment on "Geometry of the quantum set on no-signaling faces"

In Ref. [1] the authors claim that the Almost Quantum set of correlations cannot reproduce two points on the boundary of the quantum set of correlations. This claim is incorrect. The underlying issue is that the associated SDP is not strictly feasible, which makes the numerical solvers give unreliable answers. We give analytical proofs that both points are indeed reproduced by Almost Quantum.

quant-ph↗