arXiv subjects

Albert Aloy

Publications and source records attributed to Albert Aloy.

At least 19 recordsLinked to original sources

arXiv2025

Certified randomness from quantum speed limits

Quantum speed limits are usually regarded as fundamental restrictions, constraining the amount of computation that can be achieved within some given time and energy. Complementary to this intuition, here we show that these limitations are also of operational value: they enable the secure generation of certified randomness. We consider a prepare-and-measure scenario with some (experimentally determined or promised) upper bound on the energy uncertainty of the average prepared quantum state, but without any further assumptions on the devices, Hilbert space or Hamiltonian. Given that we can freely choose the time at which to apply the untrusted preparation procedure, we show that this scenario admits the generation of randomness that is secure against adversaries with additional classical information. We show how to determine the amount of certified randomness given the observed correlations, discuss how interactions with the environment are taken into account, and sketch a conceivable experimental implementation. In particular, we show that single-mode coherent states admit this kind of certification of non-zero randomness in some parameter regimes, reinforcing existing demonstrations of nonclassicality in the simple harmonic oscillator. Our results extend earlier efforts to devise semi-device-independent protocols grounded in reasonable physical assumptions, and they contribute to the understanding of time-energy uncertainty relations via their operational consequences.

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arXiv2024

Theory-independent monitoring of the decoherence of a superconducting qubit with generalized contextuality

Characterizing the nonclassicality of quantum systems under minimal assumptions is an important challenge for quantum foundations and technology. Here we introduce a theory-independent method of process tomography and perform it on a superconducting qubit. We demonstrate its decoherence without assuming quantum theory or trusting the devices by modelling the system as a general probabilistic theory. We show that the superconducting system is initially well-described as a quantum bit, but that its realized state space contracts over time, which in quantum terminology indicates its loss of coherence. The system is initially nonclassical in the sense of generalized contextuality: it does not admit of a hidden-variable model where statistically indistinguishable preparations are represented by identical hidden-variable distributions. In finite time, the system becomes noncontextual and hence loses its nonclassicality. Moreover, we demonstrate in a theory-independent way that the system undergoes non-Markovian evolution at late times. Our results extend theory-independent tomography to time-evolving systems, and show how important dynamical physical phenomena can be experimentally monitored without assuming quantum theory.

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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.

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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.

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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.

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arXiv2024

Effects of Topological Boundary Conditions on Bell Nonlocality

Bell nonlocality is the resource that enables device-independent quantum information processing tasks. It is revealed through the violation of so-called Bell inequalities, indicating that the observed correlations cannot be reproduced by any local hidden variable model. While well explored in few-body settings, the question of which Bell inequalities are best suited for a given task remains quite open in the many-body scenario. One natural approach is to assign Bell inequalities to physical Hamiltonians, mapping their interaction graph to two-body, nearest-neighbor terms. Here, we investigate the effect of boundary conditions in a two-dimensional square lattice, which can induce different topologies in lattice systems. We find a relation between the induced topology and the Bell inequality's effectiveness in revealing nonlocal correlations. By using a combination of tropical algebra and tensor networks, we quantify their detection capacity for nonlocality. Our work can act as a guide to certify Bell nonlocality in many-qubit devices by choosing a suitable Hamiltonian and measuring its ground state energy; a task that many quantum experiments are purposely built for.

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arXiv2023

Spin-bounded correlations: rotation boxes within and beyond quantum theory

How can detector click probabilities respond to spatial rotations around a fixed axis, in any possible physical theory? Here, we give a thorough mathematical analysis of this question in terms of "rotation boxes", which are analogous to the well-known notion of non-local boxes. We prove that quantum theory admits the most general rotational correlations for spins 0, 1/2, and 1, but we describe a metrological game where beyond-quantum resources of spin 3/2 outperform all quantum resources of the same spin. We prove a multitude of fundamental results about these correlations, including an exact convex characterization of the spin-1 correlations, a Tsirelson-type inequality for spins 3/2 and higher, and a proof that the general spin-J correlations provide an efficient outer SDP approximation to the quantum set. Furthermore, we review and consolidate earlier results that hint at a wealth of applications of this formalism: a theory-agnostic semi-device-independent randomness generator, an exact characterization of the quantum (2,2,2)-Bell correlations in terms of local symmetries, and the derivation of multipartite Bell witnesses. Our results illuminate the foundational question of how space constrains the structure of quantum theory, they build a bridge between semi-device-independent quantum information and spacetime physics, and they demonstrate interesting relations to topics such as entanglement witnesses, spectrahedra, and orbitopes.

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arXiv2022

Theory-independent randomness generation from spatial symmetries

We demonstrate a fundamental relation between the structures of physical space and of quantum theory: the set of quantum correlations in a rotational prepare-and-measure scenario can be derived from covariance alone, without assuming quantum physics. To show this, we consider a semi-device-independent randomness generation scheme where one of two spatial rotations is performed on an otherwise uncharacterized preparation device, and one of two possible measurement outcomes is subsequently obtained. An upper bound on a theory-independent notion of spin is assumed for the transmitted physical system. It turns out that this determines the set of quantum correlations and the amount of certifiable randomness in this setup exactly. Interestingly, this yields the basis of a theory-independent protocol for the secure generation of random numbers. Our results support the conjecture that the symmetries of space and time determine at least part of the probabilistic structure of quantum theory.

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arXiv2022

Robustness of non-locality in many-body open quantum systems

Non-locality consists in the existence of non-classical correlations between local measurements. So far, it has been investigated mostly in isolated quantum systems. Here we show that non-local correlations are present, can be detected and might be robust against noise also in many-body open quantum systems, both in the steady-state and in the transient regime. We further discuss the robustness of non-local correlations when the open quantum system undergoes repeated measurements, a relevant scenario for quantum cryptography.

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arXiv2021

Entangled symmetric states and copositive matrices

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For the simplest symmetric states, i.e., the diagonal symmetric (DS) states, it has been shown that there exists a correspondence between exceptional (non-exceptional) copositive matrices and non-decomposable (decomposable) Entanglement Witnesses (EWs). Here we show that EWs of symmetric, but not DS, states can also be constructed from extended copositive matrices, providing new examples of bound entangled symmetric states, together with their corresponding EWs, in arbitrary odd dimensions.

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arXiv2021

Applications of Quantum Randomness: From Rabi Oscillations to Fourier Axis Controlling the Musical Timbre

Randomness has attracted great interest in the field of music composition for quite some time. As early as 1962, Iannis Xenakis started exploring a stochastic approach to randomness by using computer-based interlinking probability functions to determine compositional structure, pitches and their durations. Soon after, composers and music technologists started to explore randomness with various methods of algorithmic compositions, sometimes with the help of artificial intelligence. However, in most cases, the source of randomness they used was in fact deterministic in nature. That is to say, the random numbers that they employed are imperfect in the strict sense (simply put, perfect random numbers never have repeating patterns). Moreover, the method in which they produced such randomness was extrinsic to the method in which randomness was applied. In this project, we attempt to take a further step by directly producing sound events from the genuine quantum true randomness of quantum physical systems. Through this method, we aim at achieving a new sense of aesthetic effect in music which derives from the true randomness that prevails in the natural quantum world.

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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.

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arXiv2020

Storage capacity and learning capability of quantum neural networks

We study the storage capacity of quantum neural networks (QNNs) described as completely positive trace preserving (CPTP) maps, which act on an $N$-dimensional Hilbert space. We demonstrate that QNNs can store up to $N$ linearly independent pure states and provide the structure of the corresponding maps. While the storage capacity of a classical Hopfield network scales linearly with the number of neurons, we show that QNNs can store an exponential number of linearly independent states. We estimate, employing the Gardner program, the relative volume of CPTP maps with $M$ stationary states. The volume decreases exponentially with $M$ and shrinks to zero for $M\geq N+1$. We generalize our results to QNNs storing mixed states as well as input-output relations for feed-forward QNNs. Our approach opens the path to relate storage properties of QNNs to the quantum properties of the input-output states. This paper is dedicated to the memory of Peter Wittek.

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arXiv2020

Bounding the fidelity of quantum many-body states from partial information

We formulate an algorithm to lower bound the fidelity between quantum many-body states only from partial information, such as the one accessible by few-body observables. Our method is especially tailored to permutationally invariant states, but it gives nontrivial results in all situations where this symmetry is even partial. This property makes it particularly useful for experiments with atomic ensembles, where relevant many-body states can be certified from collective measurements. As an example, we show that a $ξ^2\approx-6\;\text{dB}$ spin squeezed state of $N=100$ particles can be certified with a fidelity up to $F=0.999$, only from the measurement of its polarization and of its squeezed quadrature. Moreover, we show how to quantitatively account for both measurement noise and partial symmetry in the states, which makes our method useful in realistic experimental situations.

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arXiv2020

The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing

In this paper, we present a method to solve the quantum marginal problem for symmetric $d$-level systems. The method is built upon an efficient semi-definite program that determines the compatibility conditions of an $m$-body reduced density with a global $n$-body density matrix supported on the symmetric space. We illustrate the applicability of the method in central quantum information problems with several exemplary case studies. Namely, (i) a fast variational ansatz to optimize local Hamiltonians over symmetric states, (ii) a method to optimize symmetric, few-body Bell operators over symmetric states and (iii) a set of sufficient conditions to determine which symmetric states cannot be self-tested from few-body observables. As a by-product of our findings, we also provide a generic, analytical correspondence between arbitrary superpositions of $n$-qubit Dicke states and translationally-invariant diagonal matrix product states of bond dimension $n$.

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arXiv2019

Bell correlations at Ising quantum critical points

When a collection of distant observers share an entangled quantum state, the statistical correlations among their measurements may violate a many-body Bell inequality, demonstrating a non-local behavior. Focusing on the Ising model in a transverse-field with power-law ($1/r^α$) ferromagnetic interactions, we show that a permutationally invariant Bell inequality based on two-body correlations is violated in the vicinity of the quantum-critical point. This observation, obtained via analytical spin-wave calculations and numerical density-matrix renormalization group computations, is traced back to the squeezing of collective-spin fluctuations generated by quantum-critical correlations. We observe a maximal violation for infinite-range interactions ($α=0$), namely when interactions and correlations are themselves permutationally invariant.

cond-mat.str-el↗

arXiv2019

Optimization of device-independent witnesses of entanglement depth from two-body correlators

In a recent work [A. Aloy et al. arXiv:1807:06027 (2018)] we have considered the characterization of entanglement depth, from a device-independent perspective, in a quantum many-body system. We have shown that the inequalities introduced in [J. Tura et al. Science 344 1256 (2014)] can be used to obtain device-independent witnesses of entanglement depth and that they enjoy two key properties that allow to compute their $k$-producibility bounds more efficiently for larger system sizes, as well as yielding experimentally-friendlier device-independent witnesses of entanglement depth: they involve at most two-body correlators and they are permutationally invariant. While the main aim of our previous work was to illustrate the main ideas and applicability of the method, here we outline the details and complement its findings with detailed analysis and further case studies. Specifically, we consider the problem of finding the $k$-producible bounds of such DIWEDs under different assumptions. Not surprisingly, with the weakest assumptions, we can compute $k$-producible bounds only for relatively small number of parties; however we can still learn interesting features from these solutions that motivate the search on larger systems under the assumption that these features persist. This allows us to tackle the case where the system size eventually reaches the thermodynamic limit.

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arXiv2019

Device-independent witnesses of entanglement depth from two-body correlators

We consider the characterization of entanglement depth in a quantum many-body system from the device-independent perspective; i.e., certifying how many particles are genuinely entangled without relying on assumptions on the system itself nor on the measurements performed. We obtain device-independent witnesses of entanglement depth (DIWEDs) using the Bell inequalities introduced in [J. Tura et al., Science 344, 1256 (2014)] and compute their $k$-producibility bounds. To this end, we present two complementary methods: First, a variational one, yielding a possibly optimal $k$-producible state. Second, a certificate of optimality via a semi-definite program, based on a relaxation of the quantum marginal problem. Numerical results suggest a clear pattern on $k$-producible bounds for large system sizes, which we then tackle analytically in the thermodynamic limit. Contrary to existing DIWEDs, the ones we present here can be effectively measured by accessing only collective measurements and second moments thereof. These technical requirements are met in current experiments, which have already been performed in the context of detecting Bell correlations in quantum many-body systems of $5\cdot 10^2 \sim 5 \cdot 10^5$ atoms.

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