arXiv subjects

Giovanni Scala

Publications and source records attributed to Giovanni Scala.

At least 19 recordsLinked to original sources

arXiv2026

Finite-size Entanglement Certification via Third-Order Local Randomized Measurements

Certifying entanglement in high-dimensional systems usually requires full state tomography, whose cost grows rapidly with the system dimension. Local randomized measurements offer a scalable alternative, but existing tests based on second-order correlations access only limited information about the state. Here, we derive a finite-size entanglement certificate that extends local randomized measurements to third order. The additional third-order information reveals entanglement that remains undetected at second order, while a dimension-independent concentration bound provides rigorous control of finite-sample errors. Our result opens a practical route to extracting stronger entanglement information from experimental platforms without the dimension-dependent overhead of state tomography.

quant-ph↗

arXiv2026

Recovery-Free CHSH Nonlocality with Particle Loss

Can CHSH nonlocality survive particle loss without applying an explicit recovery operation? In principle, any deterministic recovery can be absorbed into the measurement. Operationally, we show that the answer depends on the allowed measurements on the lossy system. We distinguish flagged erasure, in which each lost particle leaves a detectable record, from unflagged deletion, in which no such record remains. For flagged erasure and survival probability $\eta>1/2$, using known quantum-capacity results, we show measurements that asymptotically approach the quantum maximum $2\sqrt2$. In contrast, for $\eta\le1/2$, CHSH violation is impossible for both loss models. Then, we construct explicit recovery-free protocols using permutation-invariant encodings built from $n$-qubit Dicke states $| D_N^n\rangle$ and measurements on the surviving particles. A one-excitation $(N=1)$ encoding violates CHSH for $\eta>1/\sqrt{2}$. Increasing the excitation number $N$ yields a family of protocols that violates CHSH for $\eta>\eta_G=(\sqrt{5}-1)/2$, with the asymptotic golden ratio approached as $N \to \infty$. Finally, we present a sparse-deletion binomial PI protocol that guarantees CHSH violation for up to $O(\sqrt n)$ deletion errors. Our results distinguish fundamental limits imposed by loss from those set by explicit measurements without recovery.

quant-ph↗

arXiv2026

Third-Order Local Randomized Measurements for Finite-size Entanglement Certification

Randomized measurements access nonlinear functionals without full tomography, yet turning third-order local single-copy data into a strong entanglement test remains difficult. We convert the reduction criterion into an experimentally measurable separability criterion by testing it on squared affine combinations of the identity, the local marginals, and the state itself. This yields a $4\times4$ matrix $\bar{\mathfrak{M}}(\rho)$ built from experimentally accessible second- and third-order local invariants. Entanglement is certified when its minimum eigenvalue $\mathcal{E}_4(\rho)$ becomes negative. We prove that all separable states satisfy $\bar{\mathfrak{M}}(\rho)\succeq0$, and that the sign of $\mathcal{E}_4(\rho)$ can be inferred from single-copy randomized measurements with dimension-independent sample complexity. For isotropic states on $d\times d$, the second-order purity criterion detects entanglement only for $p\sim d^{-1/2}$, whereas our third-order witness reaches $p\sim 2/d$, close to the separability threshold $p\sim 1/d$. A complementary nonisotropic benchmark shows that the affine marginal directions become essential once the local states are not maximally mixed.

quant-ph↗

arXiv2026

Finite-size resource scaling for learning quantum phase transitions with fidelity-based support vector machines

Quantum kernels offer a valid procedure for learning quantum phase transitions on quantum processing devices, yet issues on the scalability of the learning strategy in connection with the symmetry of the critical model have not been clarified. We derive a link between model symmetry and fidelity-kernel resource scaling. We quantify the measurement resources required to estimate fidelity-based quantum kernels for many-body ground states while preserving the structure of the resulting Gram matrix under finite-shot sampling. Crucially, we show that increasing symmetry in the underlying spin model systematically amplifies these shot requirements. Moving from the $\mathbb{Z}_2$-symmetric Ising/XY regimes to the $U(1)$-symmetric XX (and XXZ) regimes leads to stronger kernel concentration and therefore substantially larger shot costs under the same bounds. We consider a tunable one-dimensional spin-$\tfrac{1}{2}$ Hamiltonian spanning the transverse-field Ising, XY, XX, and XXZ limits, and define the kernel as the ground-state fidelity. Kernel entries are estimated using a SWAP-test estimator with $S$ shots, and we adapt the ensemble spread and concentration-avoidance shot bounds to obtain practical shot requirements in terms of the interquartile range of kernel values and a representative kernel magnitude. For the free-fermion XY/XX family, we use the closed-form Bogoliubov-angle fidelity, while for the interacting XXZ chain we compute fidelities by exact diagonalization and benchmark shot-noise effects. Our symmetry-aware bounds provide a pragmatic procedure for physics-informed quantum machine learning.

quant-ph↗

arXiv2026

Preprocessing noise in finite-size quantum key distribution

It is known that preprocessing noise may boost quantum key distribution by expanding the range of values of tolerated noise. For BB84, adding trusted noise may allow the generation of secret keys even for qubit error rate (QBER) beyond the 11% threshold in the asymptotic regime. Here we study the effect of preprocessing noise in the finite-size regime where only a limited number of signals are exchanged between Alice and Bob. We compute tight numerical lower bounds in terms of the sandwiched R\'enyi entropy of order alpha, optimized via a two-step Frank-Wolfe algorithm, in the presence of a trusted flipping probability q. We find that trusted noise improves the key rate only for a finite interval of alpha, from the alpha -> 1 limit up to alpha approx 1.4. By optimizing on the value of alpha, we determine finite-size key rates for different values of the QBER, observing enhancement due to trusted noise both in asymptotic and finite-size regimes. Finally, we determine the maximum tolerable QBER as a function of the block size.

quant-ph↗

arXiv2026

Finite-size security of QKD: comparison of three proof techniques

We compare three proof techniques for composable finite-size security of quantum key distribution under collective attacks, with emphasis on how the resulting secret-key rates behave at practically relevant block lengths. As a benchmark, we consider the BB84 protocol and evaluate finite-size key-rate estimates obtained from entropic uncertainty relations (EUR), from the asymptotic equipartition property (AEP), and from a direct finite-block analysis based on the conditional min-entropy, which we refer to as the finite-size min-entropy (FME) approach. For BB84 we show that the EUR-based bound provides the most favorable performance across the considered parameter range, while the AEP bound is asymptotically tight but can become overly pessimistic at moderate and small block sizes, where it may fail to certify a positive key. The FME approach remains effective in this small-block regime, yielding nonzero rates in situations where the AEP estimate vanishes, although it is not asymptotically optimal for BB84. These results motivate the use of FME-type analyses for continuous-variable protocols in settings where tight EUR-based bounds are unavailable, notably for coherent-state schemes where current finite-size analyses typically rely on AEP-style corrections.

quant-ph↗

arXiv2025

Finite-size secret-key rates of discrete modulation continuous-variable quantum key distribution under Gaussian attacks

Quantum conditional entropies play a fundamental role in quantum information theory. In quantum key distribution, they are exploited to obtain reliable lower bounds on the secret-key rates in the finite-size regime, against collective attacks and coherent attacks under suitable assumptions. Here we consider continuous-variable communication protocols, where the sender Alice encodes information using a discrete modulation of phase-shifted coherent states, and the receiver Bob decodes by homodyne or heterodyne detection. We compute the Petz-R\'enyi and sandwiched R\'enyi conditional entropies associated with these setups, assuming either a passive eavesdropper or one that injects thermal photons into the channel, who gathers the quantum information leaked through a lossy communication line of known or bounded transmittance. Whereas our results do not directly provide reliable key-rate estimates, they do represent useful ball-park figures. We obtain analytical or semi-analytical expressions that do not require intensive numerical calculations. These expressions serve as bounds on the key rates that may be tight in certain scenarios. We compare different estimates, including known bounds that have already appeared in the literature and new bounds. The latter are found to be tighter for very short block sizes.

quant-ph↗

arXiv2025

Entanglement detection via third-order local invariants from randomized measurements

We compute all third-order local invariants accessible via randomised measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite states with arbitrary local dimensions. The results show that third-order invariants capture inter-subsystem correlations beyond second-order spectral criteria within more feasible entanglement detection protocols than full tomography. As an example, Werner states in $d=3$ the entanglement is detected for $p>\frac 12$ at the second-order correlations, and it is improved to $p>\frac 1{\sqrt[3]{10}}$ at the third-order.

quant-ph↗

arXiv2025

The future of secure communications: device independence in quantum key distribution

In the ever-evolving landscape of quantum cryptography, Device-independent Quantum Key Distribution (DI-QKD) stands out for its unique approach to ensuring security based not on the trustworthiness of the devices but on nonlocal correlations. Beginning with a contextual understanding of modern cryptographic security and the limitations of standard quantum key distribution methods, this review explores the pivotal role of nonclassicality and the challenges posed by various experimental loopholes for DI-QKD. Various protocols, security against individual, collective and coherent attacks, and the concept of self-testing are also examined, as well as the entropy accumulation theorem, and additional mathematical methods in formulating advanced security proofs. In addition, the burgeoning field of semi-device-independent models (measurement DI--QKD, Receiver DI--QKD, and One--sided DI--QKD) is also analyzed. The practical aspects are discussed through a detailed overview of experimental progress and the open challenges toward the commercial deployment in the future of secure communications.

quant-ph↗

arXiv2024

Robustness of chaotic-light correlation imaging against turbulence

We consider an imaging scheme, inspired by microscopy, in which both correlation imaging and first-order intensity imaging can be performed simultaneously, to investigate the effects of strong turbulence on the two different kinds of images. The comparison between direct and correlation imaging in the presence of strong turbulence unambiguously revealed an advantage of the latter. Remarkably, this advantage, quantified by analyzing the visibility of periodic sample patterns, is more striking when the presence of turbulence becomes the dominant factor in determining the image resolution.

physics.optics↗

arXiv2024

Optimal and robust error filtration for quantum information processing

Error filtration is a hardware scheme that mitigates noise by exploiting auxiliary qubits and entangling gates. Although both signal and ancillas are subject to local noise, constructive interference(and in some cases post-selection) allows us to reduce the noise level in the signal qubit. Here we determine the optimal entangling unitary gates that make the qubits interfere most effectively,starting from a set of universal gates and proceeding by optimizing suitable functionals by gradient-descent or stochastic approximation. We examine how our optimized scheme behaves under imperfect implementation, where ancillary qubits may be noisy or subject to cross-talk. Even with these imperfections, we find that adding more ancillary qubits helps in protecting quantum information . We benchmark our approach against figures of merit that correspond to different applications, including entanglement fidelity, quantum Fisher information (for applications in quantum sensing),and CHSH value (for cryptographic applications), with one, two, and three ancillary qubits. With one and two ancillas we also provide analytical explicit expressions from an ansatz for the optimal unitary. We also compare our method with the recently introduced Superposed Quantum Error Mitigation (SQEM) scheme based on superposition of causal orders, and show that, for a wide range of noise strengths, our approach may outperform SQEM in terms of effectiveness and robustness.

quant-ph↗

arXiv2024

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 Gr\"obner 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 Navascu\'es--Pironio--Ac\'in hierarchy to saturate the maximum quantum violation of these inequalities.

quant-ph↗

arXiv2023

Optimality of generalized Choi maps in $M_3$

A family of linear positive maps in the algebra of $3 \times 3$ complex matrices proposed recently in Bera et al. arXiv:2212.03807 is further analyzed. It provides a generalization of a seminal Choi nondecomposable extremal map in $M_3$. We investigate when generalized Choi maps are optimal, i.e. cannot be represented as a sum of positive and completely positive maps. This property is weaker than extremality, however, it turns out that it plays a key role in detecting quantum entanglement.

quant-ph↗

arXiv2023

Insights into Quantum Contextuality and Bell Nonclassicality: A Study on Random Pure Two-Qubit Systems

We explore the relationship between Kochen-Specker quantum contextuality and Bell-nonclassicality for ensembles of two-qubit pure states. We present a comparative analysis showing that the violation of a noncontextuality inequality on a given quantum state reverberates on the Bell-nonclassicality of the considered state. In particular, we use suitable inequalities that are experimentally testable to detect quantum contextuality and nonlocality for systems in a Hilbert space of dimension $d=4$. While contextuality can be assessed on different degrees of freedom of the same particle, the violation of local realism requires parties spatially separated.

quant-ph↗

arXiv2023

On the Fidelity Robustness of CHSH--Bell Inequality via Filtered Random States

The theorem developed by John Bell constituted the starting point of a revolution that translated a philosophical question about the nature of reality into the broad and intense field of research of the quantum information technologies. We focus on a system of two qubits prepared in a random, mixed state, and we study the typical behavior of their nonlocality via the CHSH--Bell inequality. Afterward, motivated by the necessity of accounting for inefficiency in the state preparation, we address to what extent states close enough to one with a high degree of nonclassicality can violate local realism with a previously chosen experimental setup.

quant-ph↗

arXiv2023

Advantages of quantum communication revealed by the reexamination of hyperbit theory limitations

Paw{\l}owski and Winter's hyperbit theory, proposed in 2012, presented itself as an alternative to quantum theory, suggesting novel ways of redefining entanglement and classical communication paradigms. This research undertakes a meticulous reevaluation of hyperbit theory, uncovering significant operational constraints that question its equivalence with quantum mechanics. Crucially, the supposition that hyperbit theory and quantum theory are equivalent relies on the receiver having unattainable additional knowledge about the sender's laboratory, indicating that the work by Pawlowski and Winter is incorrect. This study accentuates the constraints of hyperbits in information processing and sheds light on the superiority of quantum communication, thereby advancing the investigation at the intersection of classical and quantum communication.

quant-ph↗

arXiv2023

Information theoretical perspective on the method of Entanglement Witnesses

We frame entanglement detection as a problem of random variable inference to introduce a quantitative method to measure and understand whether entanglement witnesses lead to an efficient procedure for that task. Hence we quantify how many bits of information a family of entanglement witnesses can infer about the entanglement of a given quantum state sample. The bits are computed in terms of the mutual information and we unveil there exists hidden information not \emph{efficiently} processed. We show that there is more information in the expected value of the entanglement witnesses, i.e. $\mathbb{E}[W]=\langle W \rangle_\rho$ than in the sign of $\mathbb{E}[W]$. This suggests that an entanglement witness can provide more information about the entanglement if for our decision boundary we compute a different functional of its expectation value, rather than $\mathrm{sign}\left(\mathbb{E}\right [ W ])$.

quant-ph↗

arXiv2023

Revisited aspects of the local set in CHSH Bell scenario

The Bell inequalities stand at the cornerstone of the developments of quantum theory on both the foundational and applied side. The discussion started as a way to test whether the quantum description of reality is complete or not, but it developed in such a way that a new research area stemmed from it, namely quantum information. Far from being and exhausted topic, in the present paper we present a constructive and geometrically intuitive description of the local polytope and its facets in a bipartite Bell scenario with two dichotomic measurements per party.

quant-ph↗