arXiv subjects

Guillem Müller-Rigat

Publications and source records attributed to Guillem Müller-Rigat.

16 recordsLinked to original sources

arXiv2026

Observing Bell Inequality Violation Beyond the Qubit Bound in a Spinor Bose--Einstein Condensate

Correlations allowed by quantum mechanics can defy any classical explanation, with Bell nonlocality standing as their most profound and operationally powerful manifestation. While nonlocality has been demonstrated across a wide range of platforms, in many-body systems it has remained limited to ensembles of qubits, leaving the observation of higher-dimensional multipartite Bell correlations an open challenge. Here we report the observation of qutrit Bell correlations in a spin-1 $^{87}$Rb Bose-Einstein condensate via the violation of a Bell witness based on collective spin observables only. Exploiting spin-exchange collisions in an ensemble of $N \simeq 3.1 \times 10^{4}$ atoms, we generate spin-nematic squeezing of $-11.8(7)$ dB and observe a violation that surpasses the minimum bound achievable by a collection of $N$ qubits, providing direct evidence of genuine multipartite qutrit Bell correlations. Our results establish spinor Bose-Einstein condensates as a viable platform for investigating high-dimensional Bell correlations in the many-body regime, and demonstrate that coarse-grained collective measurements suffice to certify the dimensionality of quantum correlations at macroscopic scales.

quant-ph↗

arXiv2026

Bounding the entanglement of a state from its spectrum

We introduce a framework to upper bound the entanglement content of a bipartite quantum state from its spectrum alone. Using linear maps and their inverses, we derive rigorous constraints on the maximal entanglement that can be activated under global unitary transformations. We use as entanglement quantifiers the negativity and the Schmidt number; however, our framework is general and applies to any other entanglement measure. Our approach yields compact analytical sufficient criteria for bounding the entanglement of full-rank states in arbitrary dimensions and reveals new spectral constraints on Schmidt number witnesses.

quant-ph↗

arXiv2026

Infinite multiverses and where to find them?

Have you ever watched superhero movies like Spider-Man: Into the Spider-Verse? Or played games where your choices create different outcomes? What if we told you that in the real world, something even crazier might be happening all the time, right under our noses? Imagine shrinking down to the size of an atom. What you'd see wouldn't be like our everyday world at all! This is the realm of quantum physics, where the rules we know do not apply, where things exist everywhere and nowhere at once. The moment you observe something, it starts behaving differently. In this article, we will explore two of the many possible explanations for such phenomena, namely the Copenhagen interpretation and the many-worlds interpretation of quantum physics. We will also try to answer the question of whether there are many copies of you roaming around in different universes, and why you haven't met one.

physics.pop-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

Spatial Leggett-Garg inequalities

We formulate a spatial extension of the Leggett-Garg inequality by considering three distant observers locally measuring a many-body system at three subsequent times. The spatial form is especially suitable to test the ability of quantum devices to generate spatio-temporal correlations in a Hamiltonian-agnostic manner. We illustrate our proposal for a Heisenberg chain in a magnetic field, showing indeed that the first inequality-violation time scales proportionally to the distance between measuring parties. We attribute this phenomenon to Lieb-Robinson physics and, confirming this connection, we find that violations are anticipated when increasing the interaction range. The inequality violation is readily observable in current quantum simulation platforms, particularly Rydberg atoms arrays and ultracold atoms in optical lattices. In outlook, spatial Leggett-Garg inequalities constitute a practical tool for benchmarking the complex non-relativistic dynamics of many-body quantum systems.

quant-ph↗

arXiv2025

Symmetric quantum states: a review of recent progress

Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique physical properties: they exhibit genuine multipartite entanglement and notable robustness against noise and perturbations. These features make such states particularly well-suited for a wide range of quantum information tasks. Here, we provide a pedagogic analysis of the mathematical structure and relevant physical properties of this class of states. Beyond the theoretical framework, robust tools for certifying and verifying the properties of symmetric states in experimental settings are essential. In this regard, we explore how standard techniques -- such as quantum state tomography, Bell tests, and entanglement witnesses -- can be specifically adapted for symmetric systems. Next, we provide an up-to-date overview of the most relevant applications in which these states outperform other classes of states in specific tasks. Specifically, we address their central role in quantum metrology, highlight their use in quantum error correction codes, and examine their contribution in computation and communication tasks. Finally, we present the current state-of-the-art in their experimental generation, ranging from systems of cold atoms to implementations via quantum algorithms. We also review the most significant results obtained in the different experimental realizations. Despite the notable progress made in recent years with regard to the characterisation and application of symmetric quantum states, several intriguing questions remain unsolved. We conclude this review by discussing some of these open problems and outlining promising directions for future research.

quant-ph↗

arXiv2024

Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses

Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely unknown. In this work, we employ linear maps and their inverses to derive new sufficient analytical conditions for absolute separability in arbitrary dimensions, providing extremal points of this set and improving its characterization. Additionally, we employ convex geometry optimization to refine the characterization of the set when multiple non-comparable criteria for absolute separability are available. We also address the closely related problem of characterizing the absolute PPT (positive partial transposition) set, which consists of quantum states that remain positive under partial transposition across all unitary transformations. Finally, we extend our results to multipartite states.

quant-ph↗

arXiv2024

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

We present a three-outcome permutationally-invariant 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 show how to derive from this inequality experimentally practical Bell correlation witnesses based on the measurement of collective spin components. Moreover, we present approaches that allow us to derive scalable Bell dimension witnesses, namely criteria whose violation signals the impossibility of reproducing the observed statistics by single-particle Hilbert spaces of a certain dimension.This enables the certification of genuine three-level correlations that cannot occur in two-level, i.e. qubit, systems. As an example, we show the application of these witnesses in spin-nematic squeezed states, such as the one that can be prepared in spin-1 Bose-Einstein condensates.

quant-ph↗

arXiv2024

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↗

arXiv2024

Deriving three-outcome permutationally invariant Bell inequalities

We present strategies to derive Bell inequalities valid for systems composed of many three-level parties. This scenario is formalized by a Bell experiment with $N$ observers, each of which performs one out of two possible three-outcome measurements on their share of the system. As the complexity of the set of classical correlations prohibits its full characterization in this multipartite scenario, we consider its projection to a lower dimensional subspace spanned by permutationally invariant one- and two-body observables. This simplification allows us to formulate two complementary methods for detecting nonlocality in multipartite three-level systems, both having a complexity independent of $N$. Our work can have interesting applications in the detection of Bell correlations in paradigmatic spin-1 models, as well as in experiments with solid-state systems or atomic ensembles.

quant-ph↗

arXiv2024

Introduction to quantum entanglement in many-body systems

The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them. Besides its fundamental aspect, entanglement is also a resource, fueling emergent technologies such as quantum simulators and computers. The purpose of this chapter is to give a pedagogical introduction to the topic with a special emphasis on the multipartite scenario, i.e., entanglement distributed among many degrees of freedom. Due to the combinatorial complexity of this setting, particles can interact and become entangled in a plethora of ways, which we characterize here. We start by providing the necessary mathematical tools and elementary concepts from entanglement theory. A part of this chapter will be devoted to classifying and ordering entangled states. Then, we focus on various entanglement structures useful in condensed-matter theory such as tensor-network states or symmetric states useful for quantum-enhanced sensing. Finally, we discuss state-of-the-art methods to detect and certify such correlations in experiments, with some relevant illustrative examples.

quant-ph↗

arXiv2023

Enhancing quantum state tomography via resource-efficient attention-based neural networks

Resource-efficient quantum state tomography is one of the key ingredients of future quantum technologies. In this work, we propose a new tomography protocol combining standard quantum state reconstruction methods with an attention-based neural network architecture. We show how the proposed protocol is able to improve the averaged fidelity reconstruction over linear inversion and maximum-likelihood estimation in the finite-statistics regime, reducing at least by an order of magnitude the amount of necessary training data. We demonstrate the potential use of our protocol in physically relevant scenarios, in particular, to certify metrological resources in the form of many-body entanglement generated during the spin squeezing protocols. This could be implemented with the current quantum simulator platforms, such as trapped ions, and ultra-cold atoms in optical lattices.

quant-ph↗

arXiv2023

Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach

We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system for metrology applications without complete knowledge of the quantum state. We implement the algorithm to study quantum spin ensembles. We first focus on Dicke states, where our findings challenge and complement previous results in the literature. We then investigate states generated during the one-axis twisting dynamics, where in particular we find that the metrological power of the so-called multi-headed cat states can be certified using simple collective spin observables, such as fourth-order moments for small systems, and parity measurements for arbitrary system sizes.

quant-ph↗

arXiv2023

Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems

Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement criteria. Moreover, the properties of such maps can be linked to entanglement properties of the states they detect. Here, we extend the results presented in [Phys. Rev A 93, 042335 (2016)], where sufficient separability criteria for bipartite systems were derived. In particular, we analyze the entanglement depth of an $N$-qubit system by proposing linear maps that, when applied to any state, result in a bi-separable state for the $1:(N-1)$ partitions, i.e., $(N-1)$-entanglement depth. Furthermore, we derive criteria to detect arbitrary $(N-n)$-entanglement depth tailored to states in close vicinity of the completely depolarized state (the normalized identity matrix). We also provide separability (or $1$- entanglement depth) conditions in the symmetric sector, including for diagonal states. Finally, we suggest how similar map techniques can be used to derive sufficient conditions for a set of expectation values to be compatible with separable states or local-hidden-variable theories. We dedicate this paper to the memory of the late Andrzej Kossakowski, our spiritual and intellectual mentor in the field of linear maps.

quant-ph↗

arXiv2022

Probing quantum entanglement from magnetic-sublevels populations: beyond spin squeezing inequalities

Spin squeezing inequalities (SSI) represent a major tool to probe quantum entanglement among a collection of few-level atoms, and are based on collective spin measurements and their fluctuations. Yet, for atomic ensembles of spin-$j$ atoms and ultracold spinor gases, many experiments can image the populations in all Zeeman sublevels $s=-j, -j+1, \dots, j$, potentially revealing finer features of quantum entanglement not captured by SSI. Here we present a systematic approach which exploits Zeeman-sublevel population measurements in order to construct novel entanglement criteria, and illustrate our approach on ground states of spin-1 and spin-2 Bose-Einstein condensates. Beyond these specific examples, our approach allows one to infer, in a systematic manner, the optimal permutationally-invariant entanglement witness for any given set of collective measurements in an ensemble of $d$-level quantum systems.

cond-mat.quant-gas↗

arXiv2021

Inferring Nonlinear Many-Body Bell Inequalities From Average Two-Body Correlations: Systematic Approach for Arbitrary Spin-j Ensembles

Violating Bell's inequalities (BIs) allows one to certify the preparation of entangled states from minimal assumptions -- in a device-independent manner. Finding BIs tailored to many-body correlations as prepared in present-day quantum computers and simulators is however a highly challenging endeavour. In this work, we focus on BIs violated by very coarse-grain features of the system: two-body correlations averaged over all permutations of the parties. For two-outcomes measurements, specific BIs of this form have been theoretically and experimentally studied in the past, but it is practically impossible to explicitly test all such BIs. Data-driven methods -- reconstructing a violated BI from the data themselves -- have therefore been considered. Here, inspired by statistical physics, we develop a novel data-driven approach specifically tailored to such coarse-grain data. Our approach offers two main improvements over the existing literature: 1) it is directly designed for any number of outcomes and settings; 2) the obtained BIs are quadratic in the data, offering a fundamental scaling advantage for the precision required in experiments. This very flexible method, whose complexity does not scale with the system size, allows us to systematically improve over all previously-known Bell's inequalities robustly violated by ensembles of quantum spin-$1/2$; and to discover novel families of Bell's inequalities, tailored to spin-squeezed states and many-body spin singlets of arbitrary spin-$j$ ensembles.

quant-ph↗