Searcharxiv⌕ Search

arXiv subjects

Jordi Tura

Publications and source records attributed to Jordi Tura.

At least 19 recordsLinked to original sources
arXiv2026

Two-Sided Bounds on Ground State Properties in Lattice Gauge Theories

Gauge theories describe fundamental interactions in the standard model of particle physics and build effective theories in condensed matter physics. Being notoriously hard to simulate, these theories are commonly regularized as lattice gauge theories which can be evaluated with high precision through Monte Carlo algorithms or variational methods. However, Monte Carlo algorithms are not applicable in all regimes due to the sign problem; while variational methods, quantum and classical alike, only give upper-bounds on the ground-state energy. Their precision crucially depends on the chosen ansatz. Here, we present a framework based on a hierarchy of semidefinite programs to yield increasingly good lower-bounds on the ground-state energy and propagate these bounds to extended observables like Wilson loops and mesonic strings. We demonstrate the numerical capabilities by applying the algorithm to a (1+1)-dimensional $\mathbb{Z}_2$ theory with dynamic fermionic matter and its pure-gauge version in (2+1)-dimensions. In both cases, we obtain certified intervals for the ground-state energy. For a one-dimensional system with 129 sites, the certified interval has a relative spread of $0.04\%$. For a two-dimensional system with 97 sites (corresponding to a $7 \times 8$ lattice), the relative spread is $2.08\%$. Beyond energy estimates, the proposed method provides rigorous bounds on both short- and long-range observables such as Wilson loops over multiple plaquettes and the magnitude of the mesonic string. The method can be both used as a computational microscope into many-body physics and a way to certify results of quantum simulators.

quant-ph↗
arXiv2026

An exact semidefinite characterization of the stoquasticity cone of permutationally invariant Bell operators

Bell correlations have been detected in atomic ensembles ranging from hundreds to hundreds of thousands of particles, witnessed by the permutationally invariant (PI) Bell operators. For all the operators realized so far, the maximally violating state can be brought, in a suitable basis, into a nonnegative-amplitude form. In that basis, the Bell operator is stoquastic. The coefficients parametrising these operators that at the same time lead to stoquasticity form a convex cone, the so-called stoquasticity cone. Its characterization had remained open beyond two-body operators, as for many-body operators the number of inequalities grows with the system size $n$. In this work we show that, in the thermodynamic limit, the stoquasticity cone admits an exact semidefinite characterization, valid at any operator order. The key observation is that, along each off-diagonal, the matrix elements are the values of a single univariate polynomial. Being univariate, this condition is equivalent to a linear matrix inequality, with no relaxation hierarchy. Therefore, deciding stoquasticity becomes a single semidefinite feasibility problem. As its lowest-degree instances, this description recovers the known three-hyperplane characterization for two-body operators and yields, for three-body operators, a curved boundary.

quant-ph↗
arXiv2026

Experimental certification of multipartite Bell correlations using only few-body symmetric correlations

Certifying Bell correlations in increasingly larger multipartite quantum systems is challenging because conventional Bell inequalities rely on many-body correlations, which become experimentally demanding to estimate as system size grows. Here we demonstrate that multipartite Bell correlations can be certified using few-body permutation-invariant (PI) correlations with a fixed maximal correlation order. We experimentally test few-body PI Bell correlation witnesses tailored for six- and eight-photon postselected Dicke states. The addition of a few four-body correlators is found to significantly enhance the noise tolerance compared with previously studied two-body witnesses: for instance, for six qubits, the selected witness tolerates a white-noise fraction of $p_c\approx0.301$, compared with $p_c\approx0.048$ for the best two-body PI inequality with the same two settings per party. For six and eight photons respectively, we observe violations of the witness bounds by $32$ and $8.9$ standard deviations, arising from postselected polarisation states with fidelities of $0.933(4)$ and $0.916(11)$ to the corresponding half-excitation Dicke states. The witnesses for the six- and eight-photon cases use the same symmetric two- and four-body correlators, just with different coefficients. These results demonstrate an experimentally accessible approach for certifying multipartite Bell correlations in larger systems without requiring full-body correlation measurements.

quant-ph↗
arXiv2026

Three-outcome multipartite Bell inequalities: applications to dimension witnessing and spin-nematic squeezing in many-body systems

We present a three-outcome Bell inequality which we show to be naturally suited to explore nonlocal correlations in many-body spin-1 systems or SU(3) models. In the specific, we demonstrate from this inequality an experimentally practical Bell correlation test based on the measurement of collective spin components. Next, we analyze such an inequality as a dimension witness, namely criteria whose violation signals the impossibility of reproducing the inferred correlations by Hilbert spaces of a certain dimension. In particular, our approach enables the certification of genuine three-level correlations in systems of arbitrary size, which cannot be reproduced by an ensemble of qubits. Then, we demonstrate how metrological resources, in the form of spin-nematic squeezed states as produced in spin-1 Bose Einstein condensates involving thousands of atoms, maximally violate such a witness. Moreover, we propose that the robustness of the violation can be used to certify the number of high-dimensional parties in the system. In this direction, we demonstrate that, in the thermodynamic limit, the squeezed correlations described above require the system to be composed entirely of qutrits. Our results shed light on the fundamental role of high-dimensional quantum resources in many-body systems and their application for metrological purposes.

quant-ph↗
arXiv2026

Graph Theoretic Approach to Quantum Nonstabilizerness

Detecting nonstabilizerness requires full tomography and an optimization over exponentially many stabilizer states. A limited Pauli measurement set promises resource-efficient magic certification, yet the resulting reduced stabilizer polytope is generally difficult to characterize. We trace this difficulty into two coupled obstructions: the simultaneous measurability of measurements captured by their frustration graph structure, and the consistency of sign dependencies from stabilizer formalism. We show that the sign dependencies can be discarded exactly whenever active dependencies are absent, and that perfect frustration graphs then make this reduced polytope efficiently solvable. This solvable regime derives a closed form bounded by the clique number of the frustration graph, revealing a tradeoff between witness capacity and simultaneous measurability. Clifford covariance allows rotated measurement sets to enlarge the detectable state space without raising the capacity. Graph structure therefore emerges as both a certificate of tractability and a design principle for scalable magic resource detection.

quant-ph↗
arXiv2026

Optimizing and Certifying Multipartite Permutationally Invariant Bell Inequalities

Multipartite Bell nonlocality provides a device-independent probe of many-body quantum correlations, but its characterization is limited by the rapid growth of the underlying classical and quantum optimization problems. We develop a scalable method for constructing and certifying permutationally invariant Bell inequalities using only one- and two-body correlators. The construction gives families of inequalities with robust quantum violations for general $m$ measurements as the number of parties $N$ becomes large. To improve robustness against noise, we optimize the ratio of the quantum value to the classical bound for these families in the large-$N$ limit. We then certify the resulting quantum violation using semidefinite programming. For the broad class of Bell inequalities studied here, the infinite-$N$ ratios take simple rational values for finite $m$ and converge to $\coth(1)$ as $m\to\infty$. The optimized inequalities efficiently detect many-body Bell nonlocality with collective measurements, with more measurement settings leading to stronger violations.

quant-ph↗
arXiv2026

Random Projections for Multi-Copy Quantum Algorithms

Estimating nonlinear properties of quantum states is a central task in quantum information science. Multivariate traces, $\mathrm{tr}(ρ_1 \cdots ρ_K)$, and nonlinear observables such as $\mathrm{tr}(ρ^K)$, for integer $K$, can be accessed through collective measurements on multiple state copies, but standard protocols based on swap tests require coherent operations on the full Hilbert space and become experimentally unfeasible for large systems. In this work, we introduce a framework for multi-copy measurements based on random projections onto lower-dimensional subspaces prior to the collective measurement, which is then performed only on the reduced Hilbert space. This procedure yields a tunable tradeoff between coherent quantum resources and statistical sampling overhead, allowing the amount of coherent processing to be matched to the capabilities of the underlying hardware. We derive explicit formulas relating the Haar-averaged projected moments to multivariate traces of the original states and analyze the sampling overhead induced by the projection procedure. Specifically, after compressing an $n$-qubit state to a reduced $q$-qubit subspace, estimating $\mathrm{tr}(ρ^K)$ requires approximately $O(2^{(n-q)(K-1)})$ copies of $ρ$, with each qubit projected out increasing the sampling cost by a factor of $2^{K-1}$. Our results establish how coherent multi-copy operations can be traded for additional state copies, enabling multi-copy quantum protocols to be optimized for the available hardware resources.

quant-ph↗
arXiv2026

Sector length distributions of recursively definable graph states through analytic combinatorics

The sector length distribution or Shor-Laflamme distribution (SLD) of quantum states is governed by the $k$-body correlations amongst the different systems, and has been used to study entanglement and error correction. A succinct description of a quantum state's SLD can be obtained by representing it through the coefficients of an appropriate weight enumerator polynomial, yielding bounds on fidelity under depolarizing noise and on multipartite entanglement. However, such expressions quickly grow out of hand and are generally difficult to achieve analytically, reflecting the computational hardness of the SLD. We sidestep this problem and, instead of a single state's SLDs, encode a family of quantum state's SLD as a generating function. We then find closed-form expressions for a large class of graph states which we call `recursively definable' and which include many common graphs such as path graphs, cycle graphs, star graphs, grid graphs, and more. As direct corollary, we obtain analytical expressions for such graph states' concentratable entanglement, bounds on their depolarizing fidelity, and a multipartite entanglement criterion. Our work opens up the use of generating functions and more generally analytic combinatorics to solve problems in quantum information theory.

quant-ph↗
arXiv2026

Nonlocality, Integrability and Quantum Chaos in the Spectrum of Bell Operators

We introduce a permutationally invariant multipartite Bell inequality for many-body three-level systems and use it to investigate a connection between Bell nonlocality and (lack of) quantum chaos. An associated Bell operator is then defined via Born's rule, mapping the conditional probabilities of the Bell inequality to quantum measurement operators. This allows us to interpret the Bell operator as an effective Hamiltonian, which we use to analyze its spectral statistics across different SU(3) irreducible representations and measurement choices. Surprisingly, we find that, in every irreducible representation exhibiting nonlocality, the measurement settings yielding maximal violation result in a Bell operator with Poissonian level statistics, thus signaling integrable behavior. This integrability is both unique and fragile, since generic or slightly perturbed measurements lead to the Wigner-Dyson statistics associated with chaotic behavior. Through further analysis, we are able to identify an emergent parity symmetry in the Bell operator near the point of maximal violation, providing an explanation for the observed regularity in the spectrum. These results suggest a deep interplay between optimal quantum measurements, non-local correlations, and integrability, opening new perspectives at the intersection of Bell nonlocality and quantum chaos.

quant-ph↗
arXiv2026

A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems

Estimating spectral gaps of quantum many-body Hamiltonians is a highly challenging computational task, even under assumptions of locality and translation-invariance. Yet, the quest for rigorous gap certificates is motivated by their broad applicability, ranging from many-body physics to quantum computing and classical sampling techniques. Here we present a general method for obtaining lower bounds on the spectral gap of frustration-free quantum Hamiltonians in the thermodynamic limit. We formulate the gap certification problem as a hierarchy of optimization problems (semidefinite programs) in which the certificate -- a proof of a lower bound on the gap -- is improved with increasing levels. Our approach encompasses existing finite-size methods, such as Knabe's bound and its subsequent improvements, as those appear as particular possible solutions in our optimization, which is thus guaranteed to either match or surpass them. We demonstrate the power of the method on one-dimensional spin-chain models where we observe an improvement by several orders of magnitude over existing finite size criteria in both the accuracy of the lower bound on the gap, as well as the range of parameters in which a gap is detected.

quant-ph↗
arXiv2026

Stoquastic permutationally invariant Bell operators

As Hermitian operators, many-body Bell operators can naturally be identified as many-body Hamiltonians. An important subclass of such Hamiltonians is the stoquastic class, characterized by having nonpositive off-diagonal matrix elements in a given basis. Interestingly, this property is shared by the permutationally invariant (PI) Bell operators underlying the largest Bell-correlation experiments to date. In this work, we explore the connection between many-body PI Bell operators and stoquasticity. We introduce the stoquasticity cone, which allows for a full characterization of the stoquastic parameter regimes for any PI Bell operator. We use this to show that PI Bell operators of the binary-input binary-output scenario consisting of at most three-body correlators can always be rendered stoquastic for any set of measurement parameters. Additionally, we also provide examples that use the stoquasticity cone to optimize for the quantum-classical gap. Numerical evidence suggests that the Bell operator used in the largest experiments to date is optimal with respect to stoquasticity. To the best of our knowledge, this work establishes the first connection between PI Bell operators and stoquasticity.

quant-ph↗
arXiv2026

Nonparametric Learning Non-Gaussian Quantum States of Continuous Variable Systems

Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum mechanics provides an accessible alternative by associating quantum states with classical probability distribution functions called tomograms. Despite its advantages, including compatibility with classical statistical methods, tomographic method remain underutilized due to a lack of robust estimation techniques. This work addresses this gap by introducing a non-parametric \emph{kernel quantum state estimation} (KQSE) framework for reconstructing quantum states and their trace characteristics from noisy data, without prior knowledge of the state. In contrast to existing methods, KQSE yields estimates of the density matrix in various bases, as well as trace quantities such as purity, higher moments, overlap, and trace distance, with a near-optimal convergence rate of $\tilde{O}\bigl(T^{-1}\bigr)$, where $T$ is the total number of measurements. KQSE is robust for multimodal, non-Gaussian states, making it particularly well suited for characterizing states essential for quantum science.

quant-ph↗
arXiv2026

Error and Resource Estimates of Variational Quantum Algorithms for Solving Differential Equations Based on Runge-Kutta Methods

A focus of recent research in quantum computing has been on developing quantum algorithms for differential equations solving using variational methods on near-term quantum devices. A promising approach involves variational algorithms, which combine classical Runge-Kutta methods with quantum computations. However, a rigorous error analysis, essential for assessing real-world feasibility, has so far been lacking. In this paper, we provide an extensive analysis of error sources and determine the resource requirements needed to achieve specific target errors. In particular, we derive analytical error and resource estimates for scenarios with and without shot noise, examining shot noise in quantum measurements and truncation errors in Runge-Kutta methods. Our analysis does not take into account representation errors and hardware noise, as these are specific to the instance and the used device. We evaluate the implications of our results by applying them to two scenarios: classically solving a $1$D ordinary differential equation and solving an option pricing linear partial differential equation with the variational algorithm, showing that the most resource-efficient methods are of order 4 and 2, respectively. This work provides a framework for optimizing quantum resources when applying Runge-Kutta methods, enhancing their efficiency and accuracy in both solving differential equations and simulating quantum systems.

quant-ph↗
arXiv2026

Optimizing quantum violation for multipartite facet Bell inequalities

Nonlocality shapes quantum correlations, revealed through the violation of Bell inequalities. The intersection of all valid Bell inequalities is the so-called local polytope. In multipartite systems, characterizing the local polytope quickly becomes an intractable task as the system size increases. Optimizing Bell inequalities to maximize the ratio between their quantum value and classical bound is key to understanding multipartite nonlocality. We propose a gradient-based method for this optimization. Numerical results indicate that local maxima of this ratio typically correspond to facet Bell inequalities of the local polytope. This enables an iterative search for tight and robust Bell inequalities. Applied to permutation-invariant scenarios, the method provides tight Bell inequalities with large quantum violations and facilitates experimental certification of Bell correlations without full knowledge of the local polytope. Moreover, analytical results of the maximum ratio are derived in the thermodynamic limit.

quant-ph↗
arXiv2025

Efficient graph-diagonal characterization of noisy states distributed over quantum networks via Bell sampling

Graph states are an important class of entangled states that serve as a key resource for distributed information processing and communication in quantum networks. In this work, we propose a protocol that utilizes a Bell sampling subroutine to characterize the diagonal elements in the graph basis of noisy graph states distributed across a network. Our approach offers significant advantages over direct diagonal estimation using unentangled single-qubit measurements in terms of scalability. Specifically, we prove that estimating the full vector of diagonal elements requires a sample complexity that scales linearly with the number of qubits ($\mathcal{O}(n)$), providing an exponential reduction in resource overhead compared to the best known $\mathcal{O}(2^n)$ scaling of direct estimation. Furthermore, we demonstrate that global properties, such as state fidelity, can be estimated with a sample complexity independent of the network size. Finally, we present numerical results indicating that the estimation in practice is more efficient than the derived theoretical bounds. Our work thus establishes a promising technique for efficiently estimating noisy graph states in large networks under realistic experimental conditions.

quant-ph↗
arXiv2025

Many-body $k$-local ground states as probes for unitary quantum metrology

Multipartite quantum states saturating the Heisenberg limit of sensitivity typically require full-body correlators to be prepared. On the other hand, experimentally practical Hamiltonians often involve few-body correlators only. Here, we study the metrological performances under this constraint, using tools derived from the quantum Fisher information. Our work applies to any encoding generator, also including a dependence on the parameter. We find that typical random symmetric ground states of $k$-body permutation-invariant Hamiltonians exhibit Heisenberg scaling. Finally, we establish a tradeoff between the Hamiltonian's gap, which quantifies preparation hardness, and the quantum Fisher information of the corresponding ground state.

quant-ph↗
arXiv2025

Tailoring Bell inequalities to the qudit toric code and self testing

Bell nonlocality provides a robust scalable route to the efficient certification of quantum states. Here, we introduce a general framework for constructing Bell inequalities tailored to the $\mathbb{Z}_d$ toric code for odd prime local dimensions. Selecting a suitable subset of stabilizer operators and mapping them to generalized measurement observables, we compute multipartite Bell expressions whose quantum maxima admit a sum-of-squares decomposition. We show that these inequalities are maximally violated by all states in the ground-state manifold of the $\mathbb{Z}_d$ toric code, and determine their classical (local) bounds through a combination of combinatorial tiling arguments and explicit optimization. As a concrete application, we analyze the case of $d=3$ and demonstrate that the maximal violation self-tests the full qutrit toric-code subspace, up to local isometries and complex conjugation. This constitutes, to our knowledge, the first-ever example of self-testing a qutrit subspace. Extending these constructions, we further present schemes to enhance the ratio of classical--quantum bounds and thus improve robustness to experimental imperfections. Our results establish a pathway toward device-independent certification of highly entangled topological quantum matter and provide new tools for validating qudit states in error-correcting codes and quantum simulation platforms.

quant-ph↗
arXiv2025

Boosting thermalization of classical and quantum many-body systems

Understanding and optimizing the relaxation dynamics of many-body systems is essential both for foundational studies in quantum thermodynamics and for applications such as quantum simulation and quantum computing. Efficient preparation of thermal states of a many-body Hamiltonian is governed by the spectral properties of the associated Lindbladian, in particular its spectral gap, which determines the slowest relaxation rate. In this work, we develop a systematic framework for constructing Lindbladians that prepare thermal states. Our approach reveals a simple relation between the relaxation dynamics at finite and infinite temperatures. The framework is scalable to larger system sizes when implemented using tensor-network methods. We find that efficient thermalization requires that the relaxation dynamics respect the symmetries of the thermal state, which reduces the number of free parameters. By applying gradient-based optimization to the Lindbladians, we enhance the spectral gap and thereby boost thermalization. When applied to both classical and quantum spin models, our method demonstrates a substantial enhancement of the spectral gap. For larger system sizes, our approach provides a variational upper bound and enables a certified lower bound on the minimum relaxation rate.

quant-ph↗