A panoramic survey. Our recent review traces the state of the art of distributed quantum information processing, from quantum-network primitives to distributed algorithms and the experimental platforms most likely to host them¹⁷ .

Characterizing distributed states by Bell sampling. We proposed efficient protocols to characterize graph-diagonal noisy states shared across the nodes of a quantum network using Bell-basis measurements¹⁸ , enabling scalable benchmarking of network states without global tomography.

Efficient entanglement detection via symmetries and permutation tests. We introduced an efficient measurement protocol for multipartite entanglement based on testing the action of permutations on copies of the state¹⁹ , and generalized the concept of concentratable entanglement via parallelized permutation tests²⁰ . These methods provide scalable benchmarks of multipartite correlations in regimes where full-state tomography is out of reach.

Reinforcement learning for entanglement distribution. We used reinforcement learning to optimize entanglement distribution policies in quantum repeater networks under realistic communication delays²¹ , showing the advantage of interpretable and locally coordinated strategies over naive baselines.

We develop methods to verify quantum states, devices, and correlations in a device-independent fashion. This includes techniques for self-testing, randomness certification, and entanglement depth estimation, all relying only on observed statistics and minimal assumptions.

Self-testing protocols. We contributed to the development of self-testing techniques for certifying quantum states and operations based solely on observed outcomes. This includes the SATWAP inequality for maximally entangled states²² , robust self-testing of quantum assemblages²³ , and approaches based on mutually unbiased bases²⁴ and graph states²⁵ . We also contributed to the generalization of SATWAP for GHZ states of arbitrary local dimension²⁶ . More recently we tailored Bell inequalities to the qudit toric code, obtaining self-testing statements for topological code states²⁷ .

Entanglement depth certification. We devised device-independent witnesses for certifying entanglement depth from two-body correlators²⁸ , along with optimization techniques to enhance their robustness²⁹ . We also studied the Bell correlation depth in multipartite systems³⁰ .

Randomness certification. We study the certification of quantum randomness in device-independent and semi-device-independent settings, identifying the minimal quantum resources required for secure randomness generation. We showed that in multi-input/output Bell scenarios, Bell nonlocality is not always sufficient to certify randomness, establishing a separation between the two concepts³¹ . We also provided necessary and sufficient conditions for randomness certification based on measurement incompatibility structures, linking randomness generation to hypergraph properties³² . Early ideas on the relation between randomness and nonlocality were already explored through monogamy constraints in non-signaling theories³³ .

Experimental implementations. Our theoretical tools have been applied in real-world settings, such as large-scale integrated photonics³⁴ and superconducting platforms³⁵ , providing experimentally robust certifications of entanglement and nonlocality.

This line of work began during my PhD³⁶ and remains a cornerstone of my research. It seeks to characterize and detect Bell correlations in large quantum systems using accessible observables such as low-order correlators or the energy. These correlations defy explanation by local hidden variable models and underpin device-independent quantum information.

Few-body Bell inequalities and experimental detection. We introduced permutationally^{37 38} and translationally³⁹ invariant Bell inequalities built from one- and two-body correlators, laying the foundation for scalable detection schemes. These methods enabled the first detection of Bell nonlocality in many-body spin systems, including a Bose-Einstein Condensate of 480 atoms and a thermal ensemble of 5×10⁵ atoms. More recently, Bell correlations were observed in spin systems beyond the Gaussian regime⁴⁰ .

Energy-based Bell witnesses. We showed that the ground state energy of certain spin Hamiltonians can serve as a Bell witness, enabling detection of nonlocality through energy measurements⁴¹ . The technique leverages convex optimization and dynamic programming for tight classical bounds. More recently, we proposed new optimization tools based on tropical algebra and tensor network contractions^{42 43} , studied topological effects on Bell nonlocality⁴⁴ , and developed strategies for operator bouncing between Bell operators and inequalities⁴⁵ . We have also looked at stoquastic permutationally invariant Bell operators⁴⁶ and at the optimization of quantum violations for multipartite facet Bell inequalities⁴⁷ .

Semidefinite relaxations of local sets. We proposed a hierarchy of semidefinite programs to approximate the set of local correlations from the outside, enabling benchmarking of experimental data against few-body permutationally invariant Bell inequalities⁴⁸ . These tools become indispensable when tackling richer scenarios, such as those with more outcomes or higher dimensions. We extended this framework in a tutorial on deriving three-outcome Bell inequalities⁴⁹ and applied it to dimension witnessing and spin-nematic squeezing in many-body systems⁵⁰ .

Temperature and quantum chaos. We showed that Bell correlations can persist at finite temperature in spin systems with infinite-range interactions⁵¹ , with spin-squeezed states as optimal witnesses. More recently, we proposed a Bell inequality for three-level systems and linked its violation to suppressed spectral signatures of quantum chaos⁵² , highlighting connections with random matrix theory; a work we dedicated to the memory of Fritz Haake.

Preparation and certification. We explored protocols for the adiabatic preparation and verification of tensor network states in quantum devices⁵³ . Our approach provides efficient semidefinite programming tools to certify spectral gaps along the adiabatic path and introduces a complete set of verifiable observables for scalable fidelity benchmarking in many-body quantum simulations.

Adiabatic preparation and gap engineering. We developed a method to maximize the spectral gap in adiabatic protocols by optimizing over parent Hamiltonians, enabling faster preparation of tensor network states without altering their ground state⁵⁴ . The approach applies to both injective and non-injective tensors and is demonstrated on paradigmatic examples like the AKLT and GHZ states.

Spectral gap certification. We introduced a hierarchy of semidefinite programs that yield rigorous lower bounds on the spectral gap of frustration-free Hamiltonians in the thermodynamic limit⁵⁵ . Our method generalizes and improves upon existing finite-size bounds, offering tighter certificates and extending the regime where a gap can be provably detected.

Expressivity and approximation power. We analyzed the expressive power of parameterized quantum circuits (PQCs) for function approximation, including functions in Sobolev spaces and continuous multivariate distributions^{56 57} .

Training under realistic noise. We studied how machine-learning surrogates can be trained from data produced by noisy quantum algorithms, in particular learning density functionals for the Fermi-Hubbard model from samples drawn at NISQ-typical noise levels⁵⁸ . Neural-network models proved able to generalize from surprisingly small noisy datasets, partially mitigating the heavy sampling overhead that limits quantum-data acquisition in current hardware.

Continuous-variable and generative learning. We developed nonparametric methods to learn non-Gaussian quantum states of continuous-variable systems from measurement data⁵⁹ . On the application side, we used parameterized quantum circuits as quantum generative models for financial time series with temporal correlations⁶⁰ , illustrating how PQCs can capture non-trivial classical distributions of practical interest.

Quantum marginal problem and variational constraints. We investigated the quantum marginal problem in symmetric systems and its implications for variational optimization, self-testing, and nonlocality⁶¹ . The results offer structural insights into feasible marginals and global state compatibility.

Machine learning for certification. We explored how machine learning tools can assist in certifying properties of complex many-body systems, offering data-driven certificates of entanglement or local constraints⁶² .

Many-body ground states as metrological probes. We have begun connecting our many-body and certification toolset to quantum metrology, showing that k-local ground states of suitably engineered Hamiltonians can serve as resources for unitary quantum metrology⁶³ . This line complements our work on many-body Bell correlations, where Bell witnesses derived from spin-squeezed states are themselves metrological figures of merit.

A panoramic review on symmetric quantum states. Several lines of work below converge in our recent invited review for Reports on Progress in Physics⁶⁴ , which surveys the mathematical structure and physical properties of permutationally invariant quantum states and the techniques used to characterize their entanglement, nonlocality, and tomographic structure.

Bound entanglement in symmetric states. We demonstrated the existence of PPT entangled states in symmetric multi-qubit systems, resolving a long-standing question in quantum information theory^{65 66} .

Diagonal symmetric states and conic geometry. We explored the entanglement structure of diagonal symmetric states, showing that testing separability in this class is NP-hard and naturally framed as a quadratic conic optimization problem⁶⁷ . Later, we established a link between these states and copositive matrices, connecting entanglement theory to non-decomposable witnesses and conic duality⁶⁸ .

Optimality of entanglement witnesses. Our early research explored decomposable entanglement witnesses and their relation to completely entangled subspaces and unextendible product bases⁶⁹ . We later applied these tools to test optimality and contributed to the disproof of the Structural Physical Approximation conjecture⁷⁰ .

Entanglement vs Nonlocality. We demonstrated that entanglement and nonlocality are fundamentally inequivalent for any number of parties, highlighting the subtleties between these key concepts⁷¹ .

Structural tools for multipartite entanglement. We developed linear map techniques to certify entanglement and compatibility properties in many-body systems⁷² , and introduced the concept of unextendible product operator bases as a generalization of UPBs to operator spaces⁷³ . We also used analytic combinatorics to characterize sector length distributions of recursively definable graph states⁷⁴ , linking entanglement structure to underlying graph topology.

Foundations of quantum thermodynamics. We explored the fundamental limits of energy extraction from quantum systems, including the role of entanglement in defining passive states and their maximal energetic properties⁷⁵ . This work reveals structural constraints on thermodynamic tasks at the quantum level.

Thermalization and open dynamics. We investigated the onset of thermalization in quantum many-body systems through the lens of Lindbladian dynamics and graph-theoretic techniques. Our results provide constructive bounds on convergence and thermal behavior in both classical and quantum regimes⁷⁶ .

The BIG Bell Test. I actively contributed to The BIG Bell Test, a global experiment involving more than 100,000 participants to close the freedom-of-choice loophole in Bell tests by using human randomness⁷⁷ . We designed both outreach material and infrastructure to integrate human choices into quantum experiments worldwide.

Science writing in IMTech. I contributed a pedagogical article on Bell correlations in quantum many-body systems to the IMTech Newsletter. This piece aims to make recent developments in nonlocality and symmetry accessible to a broad STEM audience, including undergraduate students and educators.

Visualizing multi-qubit states. We proposed the Bloch Sphere Binary Tree representation to visualize sets of multi-qubit pure states on a single diagram, making it easier to analyze their evolution and entanglement structure⁷⁸ . The accompanying open-source Python library enables interactive use in quantum education and research.

News & Views: Insights into Quantum Computing.
Our News & Views article in Nature Physics critically examines recent experimental demonstrations claiming quantum advantage. We highlight a tensor network algorithm that challenges these claims by efficiently simulating optical quantum experiments on classical hardware⁷⁹ , based on the original study.

Our Viewpoint in Physics discusses how realistic imperfections can actually simplify the classical simulation of quantum computers, potentially reducing the resources required. This insight significantly influences ongoing quantum computational research⁸⁰ , based on the original research.

Our recent contribution to Nature Computational Science explores advanced parallelization techniques for tensor network contraction. This method significantly enhances the speed of classical simulations of quantum systems, thus broadening computational possibilities⁸¹ , based on the original publication.

A Christmas story about quantum teleportation. We contributed a playful piece connecting quantum teleportation to the logistics of gift delivery, using Santa Claus as a vehicle to explain key ideas in quantum communication and entanglement⁸² .