arXiv subjects

Marc-Olivier Renou

Publications and source records attributed to Marc-Olivier Renou.

At least 37 records · Page 2Linked to original sources

arXiv2024

Certifying ground-state properties of quantum many-body systems

A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalisation quickly becomes impossible when increasing the system size, variational approaches are typically employed as a scalable alternative: energy is minimised over a subset of all possible states and then different physical quantities are computed over the solution state. Despite remarkable success, rigorously speaking, all what variational methods offer are upper bounds on the ground-state energy. On the other hand, so-called relaxations of the ground-state problem based on semidefinite programming represent a complementary approach, providing lower bounds to the ground-state energy. However, in their current implementation, neither variational nor relaxation methods offer provable bound on other observables in the ground state beyond the energy. In this work, we show that the combination of the two classes of approaches can be used to derive certifiable bounds on the value of any observable in the ground state, such as correlation functions of arbitrary order, structure factors, or order parameters. We illustrate the power of this approach in paradigmatic examples of 1D and 2D spin-one-half Heisenberg models. To improve the scalability of the method, we exploit the symmetries and sparsity of the considered systems to reach sizes of hundreds of particles at much higher precision than previous works. Our analysis therefore shows how to obtain certifiable bounds on many-body ground-state properties beyond energy in a scalable way.

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arXiv2024

No distributed quantum advantage for approximate graph coloring

We give an almost complete characterization of the hardness of $c$-coloring $χ$-chromatic graphs with distributed algorithms, for a wide range of models of distributed computing. In particular, we show that these problems do not admit any distributed quantum advantage. To do that: 1) We give a new distributed algorithm that finds a $c$-coloring in $χ$-chromatic graphs in $\tilde{\mathcal{O}}(n^{\frac{1}α})$ rounds, with $α= \bigl\lfloor\frac{c-1}{χ- 1}\bigr\rfloor$. 2) We prove that any distributed algorithm for this problem requires $Ω(n^{\frac{1}α})$ rounds. Our upper bound holds in the classical, deterministic LOCAL model, while the near-matching lower bound holds in the non-signaling model. This model, introduced by Arfaoui and Fraigniaud in 2014, captures all models of distributed graph algorithms that obey physical causality; this includes not only classical deterministic LOCAL and randomized LOCAL but also quantum-LOCAL, even with a pre-shared quantum state. We also show that similar arguments can be used to prove that, e.g., 3-coloring 2-dimensional grids or $c$-coloring trees remain hard problems even for the non-signaling model, and in particular do not admit any quantum advantage. Our lower-bound arguments are purely graph-theoretic at heart; no background on quantum information theory is needed to establish the proofs.

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arXiv2024

Universal device for two-qubit entangled measurements via photonic quantum walks

Sophisticated quantum measurements are fundamental to obtain a quantum advantage in many informational problems. Here, we consider the task of guessing a direction encoded in a two-qubit pure state. We experimentally demonstrate that abstention can be used to recover optimal direction guessing (measured in terms of the fidelity and maximum likelihood scores) even from non ideal states. Our protocol uses nine-step photonic quantum walks to implement the optimal five-output two-qubit collective measurements with fidelities above 0.9850. Thanks to abstention, we obtain more than a 10-fold improvement of the direction guessing scores (in terms of deviation to the optimal guessing scores). Our work demonstrates the versatility of photonic quantum walks for implementing many-qubit sophisticated measurements.

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arXiv2023

Nonlocality under Computational Assumptions

Nonlocality and its connections to entanglement are fundamental features of quantum mechanics that have found numerous applications in quantum information science. A set of correlations is said to be nonlocal if it cannot be reproduced by spacelike-separated parties sharing randomness and performing local operations. An important practical consideration is that the runtime of the parties has to be shorter than the time it takes light to travel between them. One way to model this restriction is to assume that the parties are computationally bounded. We therefore initiate the study of nonlocality under computational assumptions and derive the following results: (a) We define the set $\mathsf{NeL}$ (not-efficiently-local) as consisting of all bipartite states whose correlations arising from local measurements cannot be reproduced with shared randomness and \emph{polynomial-time} local operations. (b) Under the assumption that the Learning With Errors problem cannot be solved in \emph{quantum} polynomial-time, we show that $\mathsf{NeL}=\mathsf{ENT}$, where $\mathsf{ENT}$ is the set of \emph{all} bipartite entangled states (pure and mixed). This is in contrast to the standard notion of nonlocality where it is known that some entangled states, e.g. Werner states, are local. In essence, we show that there exist (efficient) local measurements producing correlations that cannot be reproduced through shared randomness and quantum polynomial-time computation. (c) We prove that if $\mathsf{NeL}=\mathsf{ENT}$ unconditionally, then $\mathsf{BQP}\neq\mathsf{PP}$. In other words, the ability to certify all bipartite entangled states against computationally bounded adversaries gives a non-trivial separation of complexity classes. (d) Using (c), we show that a certain natural class of 1-round delegated quantum computation protocols that are sound against $\mathsf{PP}$ provers cannot exist.

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arXiv2023

Proofs of network quantum nonlocality in continuous families of distributions

The study of nonlocality in scenarios that depart from the bipartite Einstein-Podolsky-Rosen setup is allowing to uncover many fundamental features of quantum mechanics. Recently, an approach to building network-local models based on machine learning lead to the conjecture that the family of quantum triangle distributions of [arXiv:1905.04902] did not admit triangle-local models in a larger range than the original proof. We prove part of this conjecture in the affirmative. Our approach consists in reducing the family of original, four-outcome distributions to families of binary-outcome ones, and then using the inflation technique to prove that these families of binary-outcome distributions do not admit triangle-local models. This constitutes the first successful use of inflation in a proof of quantum nonlocality in networks whose nonlocality could not be proved with alternative methods. Moreover, we provide a method to extend proofs of network nonlocality in concrete distributions of a parametrized family to continuous ranges of the parameter. In the process, we produce a large collection of network Bell inequalities for the triangle scenario with binary outcomes, which are of independent interest.

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arXiv2022

Self-testing entangled measurements in quantum networks

Self-testing refers to the possibility of characterizing an unknown quantum device based only on the observed statistics. Here we develop methods for self-testing entangled quantum measurements, a key element for quantum networks. Our approach is based on the natural assumption that separated physical sources in a network should be considered independent. This provides a natural formulation of the problem of certifying entangled measurements. Considering the setup of entanglement swapping, we derive a robust self-test for the Bell-state measurement, tolerating noise levels up to 5%. We also discuss generalizations to other entangled measurements.

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arXiv2022

Single-photon nonlocality in quantum networks

The state obtained when a single photon impinges on a balanced beamsplitter is often known as single-photon entangled and its nonlocal properties have been the subject of intense debates in the quantum optics and foundations communities. It is however clear that a standard Bell test made only of passive optical elements cannot reveal the nonlocality of this state. We show that the nonlocality of single-photon entangled states can nevertheless be revealed in a quantum network made only of beamsplitters and photodetectors. In our protocol, three single-photon entangled states are distributed in a triangle network, introducing indeterminacy in the photons' paths and creating nonlocal correlations without the need for measurements choices. We discuss a concrete experimental realisation and provide numerical evidence of the tolerance of our protocol to standard noise sources. Our results show that single-photon entanglement may constitute a promising solution to generate genuine network-nonlocal correlations useful for Bell-based quantum information protocols.

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arXiv2022

Bell nonlocality in networks

Bell's theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts predictions far beyond the traditional scenario of the Einstein-Podolsky-Rosen paradox. In the last decade, the investigation of nonlocality has moved beyond Bell's theorem to consider more sophisticated experiments that involve several independent sources which distribute shares of physical systems among many parties in a network. Network scenarios, and the nonlocal correlations that they give rise to, lead to phenomena that have no counterpart in traditional Bell experiments, thus presenting a formidable conceptual and practical challenge. This review discusses the main concepts, methods, results and future challenges in the emerging topic of Bell nonlocality in networks.

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arXiv2022

General measure for macroscopic quantum states beyond "dead and alive"

We consider the characterization of quantum superposition states beyond the pattern "dead and alive". We propose a measure that is applicable to superpositions of multiple macroscopically distinct states, superpositions with different weights as well as mixed states. The measure is based on the mutual information to characterize the distinguishability between multiple superposition states. This allows us to overcome limitations of previous proposals, and to bridge the gap between general measures for macroscopic quantumness and measures for Schrödinger-cat type superpositions. We discuss a number of relevant examples, provide an alternative definition using basis-dependent quantum discord and reveal connections to other proposals in the literature. Finally, we also show the connection between the size of quantum states as quantified by our measure and their vulnerability to noise.

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arXiv2022

On the inequivalence of the CH and CHSH inequalities due to finite statistics

Different variants of a Bell inequality, such as CHSH and CH, are known to be equivalent when evaluated on nonsignaling outcome probability distributions. However, in experimental setups, the outcome probability distributions are estimated using a finite number of samples. Therefore the nonsignaling conditions are only approximately satisfied and the robustness of the violation depends on the chosen inequality variant. We explain that phenomenon using the decomposition of the space of outcome probability distributions under the action of the symmetry group of the scenario, and propose a method to optimize the statistical robustness of a Bell inequality. In the process, we describe the finite group composed of relabeling of parties, measurement settings and outcomes, and identify correspondences between the irreducible representations of this group and properties of outcome probability distributions such as normalization, signaling or having uniform marginals.

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arXiv2022

Network Nonlocality via Rigidity of Token-Counting and Color-Matching

Network Nonlocality is the study of the Network Nonlocal correlations created by several independent entangled states shared in a network. In this paper, we provide the first two generic strategies to produce nonlocal correlations in large classes of networks without input. In the first one, called Token-Counting (TC), each source distributes a fixed number of tokens and each party counts the number of received tokens. In the second one, called Color-Matching (CM), each source takes a color and a party checks if the color of neighboring sources match. Using graph theoretic tools and Finner's inequality, we show that TC and CM distributions are rigid in wide classes of networks, meaning that there is essentially a unique classical strategy to simulate such correlations. Using this rigidity property, we show that certain quantum TC and CM strategies produce correlations that cannot be produced classicality. This leads us to several examples of Network Nonlocality without input. These examples involve creation of coherence throughout the whole network, which we claim to be a fingerprint of genuine forms of Network Nonlocality. This work extends a more compact parallel work [Nonlocality for Generic Networks, arXiv:2011.02769] on the same subject and provides all the required technical proofs.

quant-ph↗

arXiv2022

Nonlocality for Generic Networks

Bell's theorem shows that correlations created by a single entangled quantum state cannot be reproduced classically. Such correlations are called Nonlocal. They are the elementary manifestation of a broader phenomenon called Network Nonlocality, where several entangled states shared in a network create Network Nonlocal correlations. In this paper, we provide the first class of strategies producing nonlocal correlations in generic networks. In these strategies, called Color-Matching (CM), any source takes a color at random or in superposition, where the colors are labels for a basis of the associated Hilbert space. A party (besides other things) checks if the color of neighboring sources match. We show that in a large class of networks without input, well-chosen quantum CM strategies result in nonlocal correlations that cannot be produced classically. For our construction, we introduce the graph theoretical concept of rigidity of classical strategies in networks, and using the Finner inequality, establish a deep connection between network nonlocality and graph theory. In particular, we establish a link between CM strategies and the graph coloring problem. This work is extended in a longer paper, Network Nonlocality via Rigidity of Token-Counting and Color-Matching, where we introduce a second family of rigid strategies called Token-Counting, leading to network nonlocality.

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arXiv2022

Covariance Decomposition as a Universal Limit on Correlations in Networks

Parties connected to independent sources through a network can generate correlations among themselves. Notably, the space of feasible correlations for a given network, depends on the physical nature of the sources and the measurements performed by the parties. In particular, quantum sources give access to nonlocal correlations that cannot be generated classically. In this paper, we derive a universal limit on correlations in networks in terms of their covariance matrix. We show that in a network satisfying a certain condition, the covariance matrix of any feasible correlation can be decomposed as a summation of positive semidefinite matrices each of whose terms corresponds to a source in the network. Our result is universal in the sense that it holds in any physical theory of correlation in networks, including the classical, quantum and all generalized probabilistic theories.

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arXiv2022

Experimental Demonstration that No Tripartite-Nonlocal Causal Theory Explains Nature's Correlations

Quantum theory predicts the existence of genuinely tripartite-entangled states, which cannot be obtained from local operations over any bipartite entangled states and unlimited shared randomness. Some of us recently proved that this feature is a fundamental signature of quantum theory. The state $\left|{GHZ}_3\right\rangle=(\left|000\right\rangle+\left|111\right\rangle)/\sqrt{2}$ gives rise to tripartite quantum correlations which cannot be explained by any causal theory limited to bipartite nonclassical common causes of any kind (generalising entanglement) assisted with unlimited shared randomness. Hence, any conceivable physical theory which would reproduce quantum predictions will necessarily include genuinely tripartite resources. In this work, we verify that such tripartite correlations are experimentally achievable. We derive a new device-independent witness capable of falsifying causal theories wherein nonclassical resources are merely bipartite. Using a high-performance photonic $\left|{GHZ}_3\right\rangle$ states with fidelities of $ 0.9741\pm0.002$, we provide a clear experimental violation of that witness by more than $26.3$ standard deviation, under the locality and fair sampling assumption. We generalise our work to the $\left|{GHZ}_4\right\rangle$ state, obtaining correlations which cannot be explained by any causal theory limited to tripartite nonclassical common causes assisted with unlimited shared randomness.

quant-ph↗

arXiv2022

Quantum networks self-test all entangled states

Certifying quantum properties with minimal assumptions is a fundamental problem in quantum information science. Self-testing is a method to infer the underlying physics of a quantum experiment only from the measured statistics. While all bipartite pure entangled states can be self-tested, little is known about how to self-test quantum states of an arbitrary number of systems. Here, we introduce a framework for network-assisted self-testing and use it to self-test any pure entangled quantum state of an arbitrary number of systems. The scheme requires the preparation of a number of singlets that scales linearly with the number of systems, and the implementation of standard projective and Bell measurements, all feasible with current technology. When all the network constraints are exploited, the obtained self-testing certification is stronger than what is achievable in any Bell-type scenario. Our work does not only solve an open question in the field, but also shows how properly designed networks offer new opportunities for the certification of quantum phenomena.

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arXiv2021

Quantum theory based on real numbers can be experimentally falsified

While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through theories. While most theories of physics are based on real numbers, quantum theory was the first to be formulated in terms of operators acting on complex Hilbert spaces. This has puzzled countless physicists, including the fathers of the theory, for whom a real version of quantum theory, in terms of real operators, seemed much more natural. In fact, previous works showed that such "real quantum theory" can reproduce the outcomes of any multipartite experiment, as long as the parts share arbitrary real quantum states. Thus, are complex numbers really needed in the quantum formalism? Here, we show this to be case by proving that real and complex quantum theory make different predictions in network scenarios comprising independent states and measurements. This allows us to devise a Bell-like experiment whose successful realization would disprove real quantum theory, in the same way as standard Bell experiments disproved local physics.

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arXiv2021

Testing real quantum theory in an optical quantum network

Quantum theory is commonly formulated in complex Hilbert spaces. However, the question of whether complex numbers need to be given a fundamental role in the theory has been debated since its pioneering days. Recently it has been shown that tests in the spirit of a Bell inequality can reveal quantum predictions in entanglement swapping scenarios that cannot be modelled by the natural real-number analog of standard quantum theory. Here, we tailor such tests for implementation in state-of-the-art photonic systems. We experimentally demonstrate quantum correlations in a network of three parties and two independent EPR sources that violate the constraints of real quantum theory by over $4.5$ standard deviations, hence disproving real quantum theory as a universal physical theory.

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arXiv2021

Any Physical Theory of Nature Must Be Boundlessly Multipartite Nonlocal

We introduce the class of Genuinely Local Operation and Shared Randomness (LOSR) Multipartite Nonlocal correlations, that is, correlations between N parties that cannot be obtained from unlimited shared randomness supplemented by any composition of (N-1)-shared causal Generalized-Probabilistic-Theory (GPT) resources. We then show that noisy N-partite GHZ quantum states as well as the 3-partite W quantum state can produce such correlations. This proves, if the operational predictions of quantum theory are correct, that Nature's nonlocality must be boundlessly multipartite in any causal GPT. We develop a computational method which certifies that a noisy N=3 GHZ quantum state with fidelity 85 percent satisfies this property, making an experimental demonstration of our results within reach. We motivate our definition and contrast it with preexisting notions of genuine multipartite nonlocality. This work extends a more compact parallel letter [Phys. Rev. Lett. 127, 200401 (2021)] on the same subject and provides all the required technical proofs.

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