arXiv subjects

Alejandro Pozas-Kerstjens

Publications and source records attributed to Alejandro Pozas-Kerstjens.

At least 19 recordsLinked to original sources

arXiv2026

A versatile neural-network toolbox for testing Bell locality in networks

Determining whether an observed distribution of events generated in a quantum network is Bell local, i.e., if it admits an alternative realization in terms of independent local variables, is extremely challenging. Building upon arXiv:1907.10552, we develop a software solution that parameterizes local models in networks via neural networks. This allows one to leverage optimization tools available from the machine learning community in the search of network Bell nonlocality. Our solution applies to arbitrary networks, is easy to use, and includes technical improvements that significantly increase performance compared to previous implementations. We apply it to investigate nonlocality in several networks hitherto unexplored, providing insights on the corresponding quantum nonlocal sets and suggesting concrete, promising realizations of quantum nonlocal correlations.

quant-ph↗

arXiv2026

Uncountably many inequivalent maximally entangled measurements for two qutrits

Every two-qubit measurement basis composed of maximally entangled eigenstates can be transformed into the Bell basis via local unitary operations. For higher dimensions, in contrast, there exist inequivalent bases composed of maximally entangled eigenstates. Here, we provide a single-parameter family of two-qutrit maximally entangled measurement bases, and demonstrate that none of the bases are equivalent to each other under local unitaries. These bases are constructed from the continuous family of symmetric informationally complete sets of states in dimension three. By studying the local unitary bases that generate the family of two-qutrit maximally entangled measurement bases, we construct the first examples of wild error bases in the smallest dimension where these can exist. Finally, we discuss how distinct measurements in the family lead to differences in performance in several scenarios relevant in quantum information.

quant-ph↗

arXiv2026

Symmetric Localizable Multipartite Quantum Measurements from Pauli Orbits

While the structure of entangled quantum states is relatively well understood, the characterization of entangled measurements, especially in multipartite and high-dimensional settings, remains far less developed. In this work, we introduce a general approach to construct highly symmetric, locally encodable orthonormal measurement bases, as orbits of a single fiducial state under tensor-product actions of Pauli subgroups. This framework recovers the Elegant Joint Measurement-a two-qubit measurement whose local marginals form a regular tetrahedron on the Bloch sphere-as a special case, and we extend the construction to both more systems and higher dimensions. We analyze the entanglement cost required to implement these measurements locally via the Clifford hierarchy and use this criterion to classify them. We show how the symmetry of our constructions allows us to characterize their localizability, which is generally a challenging problem, and to identify certain classes of measurement bases that are efficiently localizable. Our approach offers a systematic toolkit for designing entangled measurements with rich symmetry and implementability properties.

quant-ph↗

arXiv2026

The minimal example of quantum network Bell nonlocality

In recent years, the study of Bell nonlocality has been generalized to quantum networks, where multiple independent sources distribute physical systems to distant parties who perform local measurements. In this context, a central open question is to identify the minimal network configuration in which quantum resources produce Bell nonlocal correlations. Here we address this question and show that quantum nonlocality is possible in the triangle network where the parties have no input choices and produce only binary-valued outcomes. To do so, we start by identifying a family of target distributions and proving their nonlocality. Next, we construct an explicit quantum model that reproduces the target distributions to machine precision. For this, we develop an efficient method for parameterizing quantum distributions in networks, inspired by the formalism of higher-order quantum operations. When considering the number of observed variables and their cardinality, this constitutes the smallest scenario possible that supports quantum nonlocality in networks. Moreover, by analyzing the explicit quantum model, we obtain new insights into how nonlocal distributions can be generated in quantum networks.

quant-ph↗

arXiv2026

Quantum-inspired tensor networks in machine learning models

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most relevant dependencies. Due to the formal similarity between quantum entanglement and statistical correlations, tensor networks have recently been integrated in machine learning, operating both as alternative learning architectures and as decompositions of components of neural networks. The expectation is that the theoretical understanding of tensor networks developed within quantum many-body physics leads to novel methods that offer advantages in terms of computational efficiency, explainability, or privacy. Here we review the use of tensor networks in the context of machine learning, providing a critical assessment of the state of the art, the potential advantages, and the challenges that must be overcome.

cs.LG↗

arXiv2026

Symmetric observations without symmetric causal explanations

Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is important to know whether symmetries in the observations correspond to symmetries in the underlying realization so that one can quickly discard impossible explanations. Via an explicit example, we demonstrate that, in general, symmetries cannot be exploited to reduce the hypothesis space. We use a tripartite probability distribution over binary events that is realized by using three (different) independent sources of classical randomness. We prove that even removing the condition that the sources distribute systems described by classical physics, the requirements that (i) the sources distribute the same physical systems, (ii) these physical systems respect relativistic causality, and (iii) the correlations are the observed ones are incompatible.

quant-ph↗

arXiv2026

Tensorization of neural networks for improved privacy and interpretability

We present a tensorization algorithm for constructing tensor train/matrix product state (MPS) representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the MPS representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing MPS in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.

math.NA↗

arXiv2025

Classification of joint quantum measurements based on entanglement cost of localization

Despite their importance in quantum theory, joint quantum measurements remain poorly understood. An intriguing conceptual and practical question is whether joint quantum measurements on separated systems can be performed without bringing them together. Remarkably, by using shared entanglement, this can be achieved perfectly when disregarding the post-measurement state. However, existing localization protocols typically require unbounded entanglement. In this work, we address the fundamental question: "Which joint measurements can be localized with a finite amount of entanglement?" We develop finite-resource versions of teleportation-based schemes and analytically classify all two-qubit measurements that can be localized in the first steps of these hierarchies. These include several measurements with exceptional properties and symmetries, such as the Bell state measurement and the elegant joint measurement. This leads us to propose a systematic classification of joint measurements based on entanglement cost, which we argue directly connects to the complexity of implementing those measurements. We illustrate how to numerically explore higher levels and construct generalizations to higher dimensions and multipartite settings.

quant-ph↗

arXiv2025

Local models and Bell inequalities for the minimal triangle network

Nonlocal correlations created in networks with multiple independent sources enable surprising phenomena in quantum information and quantum foundations. The presence of independent sources, however, makes the analysis of network nonlocality challenging, and even in the simplest nontrivial scenarios a complete characterization is lacking. In this work we study one of the simplest of these scenarios, namely that of distributions invariant under permutations of parties in the minimal triangle network, which features no inputs and binary outcomes. We perform an exhaustive search for triangle-local models, and from it we infer analytic expressions for the boundaries of the set of distributions that admit such models, which we conjecture to be all the tight Bell inequalities for the scenario. Armed with them and with improved outer approximations of the set, we provide insights on the existence of a classical-quantum gap in the triangle network with binary outcomes.

quant-ph↗

arXiv2024

Semidefinite programming relaxations for quantum correlations

Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science. Many otherwise intractable fundamental and applied problems can be successfully approached by means of relaxation to a semidefinite program. Here, we review such methodology in the context of quantum correlations. We discuss how the core idea of semidefinite relaxations can be adapted for a variety of research topics in quantum correlations, including nonlocality, quantum communication, quantum networks, entanglement, and quantum cryptography.

quant-ph↗

arXiv2024

Guarantees on the structure of experimental quantum networks

Quantum networks connect and supply a large number of nodes with multi-party quantum resources for secure communication, networked quantum computing and distributed sensing. As these networks grow in size, certification tools will be required to answer questions regarding their properties. In this work we demonstrate a general method to guarantee that certain correlations cannot be generated in a given quantum network. We apply quantum inflation methods to data obtained in quantum group encryption experiments, guaranteeing the impossibility of producing the observed results in networks with fewer optical elements. Our results pave the way for scalable methods of obtaining device-independent guarantees on the network structure underlying multipartite quantum protocols.

quant-ph↗

arXiv2024

Hierarchical certification of nonclassical network correlations

With the increased availability of quantum technological devices, it becomes more important to have tools to guarantee their correct nonclassical behavior. This is especially important for quantum networks, which constitute the platforms where multipartite cryptographic protocols will be implemented, and where guarantees of nonclassicality translate into security proofs. We derive linear and nonlinear Bell-like inequalities for networks, whose violation certifies the absence of a minimum number of classical sources in them. We do so, first, without assuming that nature is ultimately governed by quantum mechanics, providing a hierarchy interpolating between network nonlocality and full network nonlocality. Second we insert this assumption, which leads to results more amenable to certification in experiments.

quant-ph↗

arXiv2024

Privacy-preserving machine learning with tensor networks

Tensor networks, widely used for providing efficient representations of low-energy states of local quantum many-body systems, have been recently proposed as machine learning architectures which could present advantages with respect to traditional ones. In this work we show that tensor network architectures have especially prospective properties for privacy-preserving machine learning, which is important in tasks such as the processing of medical records. First, we describe a new privacy vulnerability that is present in feedforward neural networks, illustrating it in synthetic and real-world datasets. Then, we develop well-defined conditions to guarantee robustness to such vulnerability, which involve the characterization of models equivalent under gauge symmetry. We rigorously prove that such conditions are satisfied by tensor-network architectures. In doing so, we define a novel canonical form for matrix product states, which has a high degree of regularity and fixes the residual gauge that is left in the canonical forms based on singular value decompositions. We supplement the analytical findings with practical examples where matrix product states are trained on datasets of medical records, which show large reductions on the probability of an attacker extracting information about the training dataset from the model's parameters. Given the growing expertise in training tensor-network architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed.

cs.CR↗

arXiv2024

TensorKrowch: Smooth integration of tensor networks in machine learning

Tensor networks are factorizations of high-dimensional tensors into networks of smaller tensors. They have applications in physics and mathematics, and recently have been proposed as promising machine learning architectures. To ease the integration of tensor networks in machine learning pipelines, we introduce TensorKrowch, an open source Python library built on top of PyTorch. Providing a user-friendly interface, TensorKrowch allows users to construct any tensor network, train it, and integrate it as a layer in more intricate deep learning models. In this paper, we describe the main functionality and basic usage of TensorKrowch, and provide technical details on its building blocks and the optimizations performed to achieve efficient operation.

cs.LG↗

arXiv2023

Universal representation by Boltzmann machines with Regularised Axons

It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be numerically hard. Recently we proposed a regularisation of the connections of Boltzmann machines, in order to control the energy landscape of the model, paving a way for efficient sampling and training. Here we formally prove that such regularised Boltzmann machines preserve the ability to represent arbitrary distributions. This is in conjunction with controlling the number of energy local minima, thus enabling easy \emph{guided} sampling and training. Furthermore, we explicitly show that regularised Boltzmann machines can store exponentially many arbitrarily correlated visible patterns with perfect retrieval, and we connect them to the Dense Associative Memory networks.

cond-mat.stat-mech↗

arXiv2023

Post-quantum nonlocality in the minimal triangle scenario

We investigate network nonlocality in the triangle scenario when all three parties have no input and binary outputs. Through an explicit example, we prove that this minimal scenario supports nonlocal correlations compatible with no-signaling and independence of the three sources, but not with realisations based on independent quantum or classical sources. This nonlocality is robust to noise. Moreover, we identify the equivalent to a Popescu-Rohrlich box in the minimal triangle scenario.

quant-ph↗

arXiv2023

Bell inequalities with overlapping measurements

Which nonlocal correlations can be obtained, when a party has access to more than one subsystem? While traditionally nonlocality deals with spacelike separated parties, this question becomes important with quantum technologies that connect devices by means of small shared systems. Here we study Bell inequalities where measurements of different parties can have overlap. This allows to accommodate problems in quantum information such as the existence of quantum error correction codes in the framework of non-locality. The scenarios considered show an interesting behaviour with respect to Hilbert space dimension, overlap, and symmetry.

quant-ph↗

arXiv2023

Experimental full network nonlocality with independent sources and strict locality constraints

Nonlocality arising in networks composed of several independent sources gives rise to phenomena radically different from that in standard Bell scenarios. Over the years, the phenomenon of network nonlocality in the entanglement-swapping scenario has been well investigated and demonstrated. However, it is known that violations of the so-called bilocality inequality used in previous experimental demonstrations cannot be used to certify the non-classicality of their sources. This has put forward a stronger concept for nonlocality in networks, called full network nonlocality. Here, we experimentally observe full network nonlocal correlations in a network where the source-independence, locality, and measurement-independence loopholes are closed. This is ensured by employing two independent sources, rapid setting generation, and space-like separations of relevant events. Our experiment violates known inequalities characterizing non-full network nonlocal correlations by over five standard deviations, certifying the absence of classical sources in the realization.

quant-ph↗