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Marco Barbieri

Publications and source records attributed to Marco Barbieri.

At least 19 recordsLinked to original sources
arXiv2026

Certification of Network Quantum Sensing

The distribution of quantum sensors on quantum networks is a key enabler of quantum technologies in interferometry, gravimetry, timekeeping, biological monitoring, and beyond. Yet, guaranteeing the security of these distributed sensors over noisy, insecure networks remains a formidable challenge. Previous efforts to combine quantum metrology and cryptography have encountered an apparently unavoidable tension, proposing bounds for security which are only loosely tied to the achievable measurement performance. Here we introduce a quantum remote sensing protocol that can rigorously certify privacy and integrity of the estimation. By employing offline bilateral Pauli-twirling, our approach forces the effective quantum channel into a Bell-diagonal form, independently of the attack. Surprisingly, this also preserves metrological sensitivity without introducing additional experimental overhead. Relying solely on public communication alongside an insecure quantum link, the protocol enables legitimate users to exactly quantify their estimation error relative to an eavesdropper controlling the channels. We experimentally demonstrate this framework by estimating an optical phase using entangled photons, observing that the users' precision consistently surpasses the eavesdropper's capabilities across a broad parameter regime. By unifying quantum cryptography and metrology, our results provide a practical pathway to achieve simultaneous quantum-limited precision and rigorous information security in real-world quantum networks.

quant-ph↗
arXiv2026

Diameter bounds for finite simple Lie algebras

We prove strong and explicit diameter bounds for finite simple Lie algebras, which parallel Babai's conjecture for finite simple groups. Specifically, we show that any nonabelian finite simple Lie algebra $\mathfrak{g}$ over $\mathbf{F}_p$ has diameter $O((\log |\mathfrak{g}|)^D)$ for $D \approx 3.11$ with respect to any generating set. For absolutely simple classical Lie algebras over $\mathbf{F}_p$, we establish the sharper bound $O(\log |\mathfrak{g}|)$ when the Lie type is fixed and the generators are chosen uniformly at random.

math.RA↗
arXiv2026

The base size of vertex-transitive cubic graphs

We prove that if $Γ$ is a finite connected vertex-transitive cubic graph, then either $|VΓ| \le 90$, or $Γ$ is a split Praeger--Xu graph, or there exist two vertices $α$ and $β$ such that the identity is the only automorphism of $Γ$ fixing both $α$ and $β$.

math.CO↗
arXiv2026

Quantum noise in ranging with optical pulses

Optical frequency combs combine ultrashort pulse duration and phase stability, making them powerful resources for high-precision ranging even when affected by atmospheric dispersion. It has been established that by classical modal engineering and mdoe-sensitive detection sensitivity to distance at the standard limit can be achieved, however attaining improved uncertainties by the use of squeezing has not been explored. Here, we apply an effective Hamiltonian framework to the problem of ranging with quantum frequency combs in order to derive the associated precision bounds for distance estimation. We analyse the role of intensity anti-squeezing and temporal beam shaping, and find that quantum solutions may be appealing mostly for short-distance applications.

quant-ph↗
arXiv2026

On the expected value of energy in groups

We obtain explicit upper and lower bounds for the expected action energy associated with a pair $({\sf A},{\sf Δ})$ of subsets sampled uniformly at random from a permutation group and its domain, respectively. We then specialize these bounds to multiplicative energy in several settings. In particular, we derive sharp asymptotic formulae for the expected energy of pairs of the form $({\sf A},{\sf A})$ and $({\sf A},{\sf A}^{-1})$. Finally, we apply these estimates to derive probabilistic results on the existence of subsets with large growth and to compare the typical behaviour of the cardinalities of the sets $|{\sf A}^{\ast 2}|$ and $|{\sf A}{\sf A}^{-1}|$.

math.GR↗
arXiv2026

Strong convergence of random representations of free products of finite groups

We extend the polynomial method of Chen--Garza-Vargas--Tropp--van Handel and Magee--Puder--van Handel for operator-norm bounds in random permutation models to the setting where torsion is present. The main new feature is that asymptotic expansion of traces naturally involves fractional powers of $N$ rather than an ordinary Laurent series. We formulate fractional-power analogues of the method's key hypotheses and prove they lead to strong convergence. We verify these analogues for free products of finite groups $Γ=G_1*\cdots*G_m$. Concretely, for a uniformly random $ϕ_N\in{\rm hom}(Γ,{\rm Sym}(N))$, set $π_N = {\rm std} \circ ϕ_N$, where ${\rm std}$ denotes the standard $(N-1)$-dimensional representation of ${\rm Sym}(N)$ (the permutation representation with the trivial subrepresentation removed). We deduce strong convergence of $π_N$ to the left regular representation of $Γ$. As applications, we obtain asymptotically sharp spectral gaps for the associated random Schreier graphs, including almost Ramanujan behavior for $C_2*C_2*C_2$ and an explicit non-Ramanujan limiting spectral radius for $C_2*C_3 \cong {\rm PSL}_2({\bf Z})$.

math.SP↗
arXiv2026

Measurement compatibility in multiparameter quantum interferometry

The Cramér-Rao bound captures completely the performance of single-parameter quantum sensors. On the other hand, its extension to multiple parameters demands more caution. Different aspects need to be captured at once, including, critically, compatibility. In this article we consider compatibility in quantum interferometry for an important class of probe states, measured by double homodyne or photon counters, standard benchmarks for these applications. We include the presence of loss and phase diffusion in the estimation of a phase. Our results illustrate how different weighting of the precision on individual parameters affects their compatibility, adding to the list of considerations for quantum multiparameter estimation.

quant-ph↗
arXiv2025

Separating subsets from their images

Let $G$ be a transitive permutation group acting on $Ω$. In this paper, we introduce and study the parameter ${\bf m}(G)$, which denotes the size of the smallest set of points $A$ such that, for every permutation $g\in G$, $A \cap A^g$ is nonempty. In particular, we focus on deriving general bounds for arbitrary transitive groups, and on the asymptotic behaviour of certain families of primitive groups. We also provide a classification of transitive groups with ${\bf m}(G)$ largest possible, namely with ${\bf m}(G)=\lceil (|Ω|+1) / 2 \rceil$.

math.GR↗
arXiv2025

Bayesian stepwise estimation of qubit rotations

This work investigates Bayesian stepwise estimation (Se) for measuring the two parameters of a unitary qubit rotation. While asymptotic analysis predicts a precision advantage for SE over joint estimation (JE) in regimes where the quantum Fisher information matrix is near-singular ("sloppy" models), we demonstrate that this advantage is mitigated within a practical Bayesian framework with limited resources. We experimentally implement a SE protocol using polarisation qubits, achieving uncertainties close to the classical Van Trees bounds. However, comparing the total error to the ultimate quantum Van Trees bound for JE reveals that averaging over prior distributions erases the asymptotic SE advantage. Nevertheless, the stepwise strategy retains a significant practical benefit as it operates effectively with simple, fixed measurements, whereas saturating the JE bound typically requires complex, parameter-dependent operations.

quant-ph↗
arXiv2025

Private Remote Phase Estimation over a Lossy Quantum Channel

Private remote quantum sensing (PRQS) aims at estimating a parameter at a distant location by transmitting quantum states on an insecure quantum channel, limiting information leakage and disruption of the estimation itself from an adversary. Previous results highlighted that one can bound the estimation performance in terms of the observed noise. However, if no assumptions are placed on the channel model, such bounds are very loose and severely limit the estimation. We propose and analyse a PRQS using, for the first time to our knowledge, continuous-variable states in the single-user setting. Assuming a typical class of lossy attacks and employing tools from quantum communication, we calculate the true estimation error and privacy of our protocol, both in the asymptotic limit of many channel uses and in the finite-size regime. Our results show that a realistic channel-model assumption, which can be validated with measurement data, allows for a much tighter quantification of the estimation error and privacy for all practical purposes.

quant-ph↗
arXiv2025

Quasirandom and quasisimple groups

Fix $\varepsilon > 0$. We say that a finite group $G$ is $\varepsilon$-quasirandom if every nontrivial irreducible complex representation of $G$ has degree at least $|G|^\varepsilon$. In this paper, we give a structure theorem for large $\varepsilon$-quasirandom groups, and we completely classify the $\frac{1}{5}$-quasirandom groups.

math.GR↗
arXiv2025

Controlling Sloppiness in Two-Phase Estimation with a Tunable Weak Measurement

The description of complex systems requires a progressively larger number of parameters. However, in practice, it often happens that a small subset of parameters suffices to describe the dynamics of the system itself: these combinations are usually referred to as \textit{stiff} combinations. In turn, the remaining combinations, called \textit{sloppy}, only play a minor role in the dynamics of the system, hence provide little information on it. While this effect can reduce model complexity, it can also limit the estimation precision when the stiff and sloppy combinations are unknown to the experimenter, and one is forced to estimate the potentially sloppy model parameters. We explored how such a sloppy behavior can be controlled and counteracted via quantum weak measurements in the estimation of two sequential phases. We showed that the introduction of a weak measurement of variable strength in-between the two phases allows to switch from a fully sloppy setup to a fully determined one where both phases can be estimated with quantum-limited precision. Our work provides an important insight of sloppiness detection in quantum systems, with promising applications in quantum metrology and imaging, as well as to quantum security and quantum monitoring.

quant-ph↗
arXiv2025

Photon-starved polarimetry via functional classical shadows

Polarimetry and optical imaging techniques face challenges in photon-starved scenarios, where the low number of detected photons imposes a trade-off between image resolution, integration time, and sample sensitivity. Here we introduce a quantum-inspired method, functional classical shadows, for reconstructing a polarization profile in the low photon-flux regime. Our method harnesses correlations between neighbouring datapoints, based on the recent realisation that machine learning can estimate multiple physical quantities from a small number of non-identical samples. This is applied to the experimental reconstruction of polarization as a function of the wavelength. Although the quantum formalism helps structuring the problem, our approach suits arbitrary intensity regimes.

quant-ph↗
arXiv2025

Flexible $3$-valent graphs of even girth

We prove the existence of a connected flexible $3$-valent vertex-transitive graph of girth $2\ell$ for every integer $\ell$. We also give a constructive proof if $\ell$ is prime.

math.GR↗
arXiv2025

Thresholded quantum LIDAR in turbolent media

Light detection and ranging is a key technology for a number of applications, from relatively simple distance ranging to environmental monitoring. When dealing with low photon numbers an important issue is the improvement of the signal- to-noise-ratio, which is severely affected by external sources whose emission is captured by the detection apparatus. In this paper, we present an extension of the technique developed in [Phys. Rev. Lett. 123, 203601] to the effects caused by the propagation of light through a turbulent media, as well as the detection through photon counting devices bearing imperfections in terms of efficiency and number resolution. Our results indicate that even less performing technology can result in a useful detection scheme.

quant-ph↗
arXiv2025

Tutorial: Optical quantum metrology

The purpose of quantum technologies is to explore how quantum effects can improve on existing solutions for the treatment of information. Quantum photonics sensing holds great promises for reaching a more efficient trade-off between invasivity and quality of the measurement, when compared with the potential of classical means. This tutorial is dedicated to presenting how this advantage is brought about by nonclassical light, examining the basic principles of parameter estimation and reviewing the state of the art.

quant-ph↗
arXiv2025

Quasiprobability distributions with weak measurements

We discuss and experimentally demonstrate the role of quantum coherence in a sequence of two measurements collected at different times using weak measurements. For this purpose, we have realized a weak-sequential measurement protocol with photonic qubits, where the first measurement is carried out as a positive operator-valued measure, whereas the second one is a projective operation. We determine the quasiprobability distributions associated to this procedure using both the commensurate and the Margenau-Hill quasiprobabilities approaches. By tuning the weak measurements, we obtain a quasidistribution that may or may not exhibit negative parts, depending on the suitability of a contextual model for describing the experiment. Our results show how quasidistributions may find application in inspecting quantum monitoring, when part of the initial quantum coherence needs to be preserved.

quant-ph↗