arXiv subjects

Elie Wolfe

Publications and source records attributed to Elie Wolfe.

At least 19 recordsLinked to original sources

arXiv2026

Coordination Requires a Common Cause in Quantum Theory

We propose a novel causal principle that is a genuinely multipartite extension of Reichenbach's common cause principle, namely, the coordination principle: parties in a network can achieve perfect randomized coordination--in particular, agree on a uniformly random output--only if they all share a common cause. We show that this principle does not follow from the standard no-signaling and independence principles by providing an explicit theory satisfying all these principles while violating the coordination principle. Strikingly, we prove that the coordination principle holds, however, in quantum theory for four parties, and derive noise-tolerant Bell-like inequalities that certify a common cause. We then extend these results to a genuinely quantum coordination task, showing that the four-partite GHZ state requires a quantum common cause which can also be certified by experimentally accessible Bell-like inequalities. A companion paper generalizes these results for N parties, proving that the coordination principle is satisfied in general for quantum theory.

quant-ph↗

arXiv2026

A missing causal principle: Coordination

We introduce the coordination principle, which states that perfect coordination, in the form of agreement on a uniformly random output, among N parties is possible only if they share a common cause. This principle is purely causal and can be viewed as a multipartite generalization of Reichenbach's common cause principle. We prove that quantum information theory satisfy the coordination principle in any network, and derive noise-tolerant Bell-like inequalities that certify the presence of a common cause. We further show that the principle is not a consequence of no-signaling and independence alone by constructing a concrete operational probabilistic theory that obeys both principles while still allowing perfect coordination without a common cause. This possibility arises only in fully general causal scenarios with intermediate transformations between preparations and measurements. We also formulate a genuinely quantum coordination task, showing that the preparation of a multipartite GHZ state requires a quantum common cause, which can be certified by Bell-like inequalities which are experimentally testable. Finally, we discuss the open problem of finding a quantitative, noise-tolerant version of the coordination principle that constrains approximate coordination in any reasonable causal theory. This work is the extended version of the more compact letter and provides all the technical details of the proofs.

quant-ph↗

arXiv2025

Certifying Randomness or its Lack Thereof for General Network Scenarios

The certification of intrinsic randomness is foundational to quantum information theory and central in many practical applications thereof, such as in the generation of unquestionably random numbers and in cryptographic protocols. Device-independent randomness certification based on violations of Bell inequalities has been thoroughly investigated within the standard Bell scenario. In this work, we aim to extend this line of research by exploring randomness certification in more general causal structures, namely, network scenarios. To address this task, we demonstrate how the computational tool known as the inflation technique can be adapted. As proof of concept, we use inflation to certify randomness relative to a beyond-quantum adversary for sample probability distributions obtained in the bilocality and triangle scenarios. Complementarily, we also provide computational methods for the problem of certifying an absence of randomness, which should not be conflated with certifying the classicality of a given probability distribution. We conclude with a discussion of conceptual subtleties regarding randomness certification in networks, highlighting important open problems in this nascent research field.

quant-ph↗

arXiv2025

Distinguishability of causal structures under latent confounding and selection

Statistical relationships in observed data can arise for several different reasons: the observed variables may be causally related, they may share a latent common cause, or there may be selection bias. Each of these scenarios can be modelled using different causal graphs. Not all such causal graphs, however, can be distinguished by experimental data. In this paper, we formulate the equivalence class of causal graphs as a novel graphical structure, the selected-marginalized directed graph (smDG). That is, we show that two directed acyclic graphs with latent and selected vertices have the same smDG if and only if they are indistinguishable, even when allowing for arbitrary interventions on the observed variables. As a substitute for the more familiar d-separation criterion for DAGs, we provide an analogous sound and complete separation criterion in smDGs for conditional independence relative to passive observations. Finally, we provide a series of sufficient conditions under which two causal structures are indistinguishable when there is only access to passive observations.

math.ST↗

arXiv2025

Upper Bounding Hilbert Space Dimensions which can Realize all the Quantum Correlations

We introduce novel upper bounds on the Hilbert space dimensions required to realize quantum correlations in Bell scenarios. We start by considering bipartite cases wherein one of the two parties has two settings and two outcomes. Regardless of the number of measurements and outcomes of the other party, the Hilbert space dimension of the first party can be limited to two while still achieving all convexly extremal quantum correlations. We then leverage Schmidt decomposition to show that the remaining party can losslessly also be restricted to a qubit Hilbert space. We then extend this idea to multipartite scenarios. We also adapt our results to provide upper bounds of local Hilbert space dimensions to achieve any quantum correlation, including convexly non-extremal correlations, by utilizing Caratheodory's theorem. Finally, we generalize our results to nonstandard Bell scenarios with communication. Taken together, our results fill in several previously unresolved aspects of the problem of determining sufficient Hilbert space dimensionality, expanding the collection of scenarios for which finite-dimensional quantum systems are known to be sufficient to reproduce any quantum correlation.

quant-ph↗

arXiv2025

The observational partial order of causal structures with latent variables

For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the visible variables realizable by the second. Knowing such dominance relations is useful for adjudicating between these structures given observational data. Here, we consider the problem of determining the partial order of equivalence classes of causal structures with latent variables relative to observational dominance. We provide a complete characterization of the dominance order in the case of three visible variables, and a partial characterization in the case of four visible variables. Our techniques also help to identify which observational equivalence classes have a set of realizable distributions that is characterized by nontrivial inequality constraints, analogous to Bell inequalities and instrumental inequalities. We find evidence that as one increases the number of visible variables, the equivalence classes satisfying nontrivial inequality constraints become ubiquitous. (Because such classes are the ones for which there can be a difference in the distributions that are quantumly and classically realizable, this implies that the potential for quantum-classical gaps is also ubiquitous.) Furthermore, we find evidence that constraint-based causal discovery algorithms that rely solely on conditional independence constraints have a significantly weaker distinguishing power among observational equivalence classes than algorithms that go beyond these (i.e., algorithms that also leverage nested Markov constraints and inequality constraints).

stat.ML↗

arXiv2025

Fully quantum inflation: quantum marginal problem constraints in the service of causal inference

Consider the problem of deciding, for a particular multipartite quantum state, whether or not it is realizable in a quantum network with a particular causal structure. This is a fully quantum version of what causal inference researchers refer to as the problem of causal discovery. In this work, we introduce a fully quantum version of the inflation technique for causal inference, which leverages the quantum marginal problem. The primary example by which we illustrate the utility of this method is testing compatibility of tripartite quantum states with the quantum network known as the triangle scenario. We show, in particular, how the method yields a complete classification of pure three-qubit states into those that are and those that are not compatible with the triangle scenario. We also provide some illustrative examples involving mixed states and some where one or more of the systems is higher-dimensional. Furthermore, we examine the question of when the incompatibility of a multipartite quantum state with a causal structure can be inferred from the incompatibility of a joint probability distribution induced by implementing measurements on each subsystem. Finally, we present a family of networks, which include the triangle scenario as a special case, for which causal compatibility constraints can be derived.

quant-ph↗

arXiv2024

Distinguishing quantum causal scenarios with indistinguishable classical analogs: The significance of intermediate latents

The use of graphical models to represent causal hypotheses has enabled revolutionary progress in the study of the foundations of quantum theory. Here we consider directed acyclic graphs each of which contains both nodes representing observed variables as well as nodes representing latent or hidden variables. When comparing distinct causal structures, a natural question to ask is if they can explain distinct sets of observable distributions or not. Statisticians have developed a great variety of tools for resolving such questions under the assumption that latent nodes are interpreted classically. Here we highlight how the change to a quantum interpretation of the latent nodes induces distinctions between causal scenarios that would be classically indistinguishable. We especially concentrate on quantum scenarios containing latent nodes with at least one latent parent, a.k.a. possessing intermediate latents. This initial survey demonstrates that many such quantum processes can be operationally distinguished by considerations related to monogamy of nonlocality, especially when computationally aided by a hierarchy of semidefinite relaxations which we tailor for the study of such scenarios. We conclude by clarifying the challenges that prevent the generalization of this work, calling attention to open problems regarding observational (in)equivalence of quantum causal structures with intermediate latents.

quant-ph↗

arXiv2024

On the physics of nested Markov models: a generalized probabilistic theory perspective

Determining potential probability distributions with a given causal graph is vital for causality studies. To bypass the difficulty in characterizing latent variables in a Bayesian network, the nested Markov model provides an elegant algebraic approach by listing exactly all the equality constraints on the observed variables. However, this algebraically motivated causal model comprises distributions outside Bayesian networks, and its physical interpretation remains vague. In this work, we inspect the nested Markov model through the lens of generalized probabilistic theory, an axiomatic framework to describe general physical theories. We prove that all the equality constraints defining the nested Markov model are valid theory-independently. At the same time, not every distribution within the nested Markov model is implementable, not even via exotic physical theories associated with generalized probability theories (GPTs). To interpret the origin of such a gap, we study three causal models standing between the nested Markov model and the set of all distributions admitting some GPT realization. Each of the successive three models gives a strictly tighter characterization of the physically implementable distribution set; that is, each successive model manifests new types of GPT-inviolable constraints. We further demonstrate each gap through a specially chosen illustrative causal structure. We anticipate our results will enlighten further explorations on the unification of algebraic and physical perspectives of causality.

quant-ph↗

arXiv2024

Everything that can be learned about a causal structure with latent variables by observational and interventional probing schemes

What types of differences among causal structures with latent variables are impossible to distinguish by statistical data obtained by probing each visible variable? If the probing scheme is simply passive observation, then it is well-known that many different causal structures can realize the same joint probability distributions. Even for the simplest case of two visible variables, for instance, one cannot distinguish between one variable being a causal parent of the other and the two variables sharing a latent common cause. However, it is possible to distinguish between these two causal structures if we have recourse to more powerful probing schemes, such as the possibility of intervening on one of the variables and observing the other. Herein, we address the question of which causal structures remain indistinguishable even given the most informative types of probing schemes on the visible variables. We find that two causal structures remain indistinguishable if and only if they are both associated with the same mDAG structure (as defined by Evans (2016)). We also consider the question of when one causal structure dominates another in the sense that it can realize all of the joint probability distributions that can be realized by the other using a given probing scheme. (Equivalence of causal structures is the special case of mutual dominance.) Finally, we investigate to what extent one can weaken the probing schemes implemented on the visible variables and still have the same discrimination power as a maximally informative probing scheme.

stat.ML↗

arXiv2024

Escaping the Shadow of Bell's Theorem in Network Nonlocality

The possibility of nonclassicality in networks unrelated to Bell's original eponymous theorem has recently attracted significant interest. Here, we identify a sufficient condition for being "outside the shadow of Bell's theorem" and introduce a testable criterion capable of certifying the novelty of instances of network-nonclassicality which we call minimal network nonclassicality. We provide examples of minimally network nonclassical correlations realizable in quantum theory as well as examples coming from more exotic operational probabilistic theories. In particular, we apply these concepts to the simplest configuration of the 3-chain scenario (a.k.a. the bilocality scenario) to prove that certain correlations have escaped the shadow of Bell's theorem. While some of the examples herein are unprecedented, we also revisit more familiar examples of network nonclassicality in order to highlight the contrast between our approach versus prior approaches with respect to assessing novelty.

quant-ph↗

arXiv2024

Quantum Non-classicality from Causal Data Fusion

Bell's theorem, a cornerstone of quantum theory, shows that quantum correlations are incompatible with a classical theory of cause and effect. Through the lens of causal inference, it can be understood as a particular case of causal compatibility, which delves into the alignment of observational data with a given causal structure. Here, we explore the problem of causal data fusion that aims to piece together data tables collected under heterogeneous conditions. We investigate the quantum non-classicality that emerges when integrating both passive observations and interventions within an experimental setup. Referred to as "non-classicality from data fusion," this phenomenon is identified and scrutinized across all latent exogenous causal structures involving three observed variables. Notably, we demonstrate the existence of quantum non-classicality resulting from data fusion, even in scenarios where achieving standard Bell non-classicality is impossible. Furthermore, we showcase the potential for attaining non-classicality across multiple interventions using quantum resources. This work extends a more compact parallel letter on the same subject and provides all the required technical proofs.

quant-ph↗

arXiv2024

Causal Data Fusion with Quantum Confounders

From the modern perspective of causal inference, Bell's theorem -- a fundamental signature of quantum theory -- is a particular case where quantum correlations are incompatible with the classical theory of causality, and the generalization of Bell's theorem to quantum networks has led to several breakthrough results and novel applications. Here, we consider the problem of causal data fusion, where we piece together multiple datasets collected under heterogeneous conditions. In particular, we show quantum experiments can generate observational and interventional data with a non-classical signature when pieced together that cannot be reproduced classically. We prove this quantum non-classicality emerges from the fusion of the datasets and is present in a plethora of scenarios, even where standard Bell non-classicality is impossible. Furthermore, we show that non-classicality genuine to the fusion of multiple data tables is achievable with quantum resources. Our work shows incorporating interventions -- a central tool in causal inference -- can be a powerful tool to detect non-classicality beyond the violation of a standard Bell inequality. In a companion article "Quantum Non-classicality from Causal Data Fusion", we extend our investigation considering all latent exogenous causal structures with 3 observable variables.

quant-ph↗

arXiv2024

Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

The formalism of generalized probabilistic theories (GPTs) was originally developed as a way to characterize the landscape of conceivable physical theories. Thus, the GPT describing a given physical theory necessarily includes all physically possible processes. We here consider the question of how to provide a GPT-like characterization of a particular experimental setup within a given physical theory. We show that the resulting characterization is not generally a GPT in and of itself-rather, it is described by a more general mathematical object that we introduce and term an accessible GPT fragment. We then introduce an equivalence relation, termed cone equivalence, between accessible GPT fragments (and, as a special case, between standard GPTs). We give a number of examples of experimental scenarios that are best described using accessible GPT fragments, and where moreover cone-equivalence arises naturally. We then prove that an accessible GPT fragment admits of a classical explanation if and only if every other fragment that is cone-equivalent to it also admits of a classical explanation. Finally, we leverage this result to prove several fundamental results regarding the experimental requirements for witnessing the failure of generalized noncontextuality. In particular, we prove that neither incompatibility among measurements nor the assumption of freedom of choice is necessary for witnessing failures of generalized noncontextuality, and, moreover, that such failures can be witnessed even using arbitrarily inefficient detectors.

quant-ph↗

arXiv2024

Contextuality without incompatibility

The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker noncontextuality, one does indeed require sets of incompatible measurements. However, a more broadly applicable notion of classicality is the existence of a generalized-noncontextual ontological model. In particular, this notion can imply constraints on the representation of outcomes even within a single nonprojective measurement. We leverage this fact to demonstrate that measurement incompatibility is neither necessary nor sufficient for proofs of the failure of generalized noncontextuality. Furthermore, we show that every proof of the failure of generalized noncontextuality in a quantum prepare-measure scenario can be converted into a proof of the failure of generalized noncontextuality in a corresponding scenario with no incompatible measurements.

quant-ph↗

arXiv2024

A linear program for testing nonclassicality and an open-source implementation

A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an open-source implementation of it which tests whether or not any given prepare-measure experiment is classically-explainable in this sense. The input to the program is simply an arbitrary set of quantum states and an arbitrary set of quantum effects; the program then determines if the Born rule statistics generated by all pairs of these can be explained by a classical (noncontextual) model. If a classical model exists, it provides an explicit model. If it does not, then it computes the minimal amount of noise that must be added such that a model does exist, and then provides this model. We generalize all these results to arbitrary generalized probabilistic theories (and accessible fragments thereof) as well; indeed, our linear program is a test of simplex-embeddability.

quant-ph↗

arXiv2023

Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory

A standard approach to quantifying resources is to determine which operations on the resources are freely available, and to deduce the partial order over resources that is induced by the relation of convertibility under the free operations. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, i.e., entanglement, then the common assumption is that the appropriate choice of free operations is Local Operations and Classical Communication (LOCC). We here advocate for the study of a different choice of free operations, namely, Local Operations and Shared Randomness (LOSR), and demonstrate its utility in understanding the interplay between the entanglement of states and the nonlocality of the correlations in Bell experiments. Specifically, we show that the LOSR paradigm (i) provides a resolution of the anomalies of nonlocality, wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails new notions of genuine multipartite entanglement and nonlocality that are free of the pathological features of the conventional notions, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which generalizes and simplifies prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. The resource-theoretic perspective also clarifies why it is neither surprising nor problematic that there are mixed entangled states which do not violate any Bell inequality. Our results motivate the study of LOSR-entanglement as a new branch of entanglement theory.

quant-ph↗

arXiv2023

Relating Wigner's Friend Scenarios to Nonclassical Causal Compatibility, Monogamy Relations, and Fine Tuning

Nonclassical causal modeling was developed in order to explain violations of Bell inequalities while adhering to relativistic causal structure and faithfulness -- that is, avoiding fine-tuned causal explanations. Recently, a no-go theorem that can be viewed as being stronger than Bell's theorem has been derived, based on extensions of the Wigner's friend thought experiment: the Local Friendliness (LF) no-go theorem. Here we show that the LF no-go theorem poses formidable challenges for the field of causal modeling, even when nonclassical and/or cyclic causal explanations are considered. We first recast the LF inequalities, one of the key elements of the LF no-go theorem, as special cases of monogamy relations stemming from a statistical marginal problem. We then further recast LF inequalities as causal compatibility inequalities stemming from a nonclassical causal marginal problem, for a causal structure implied by well-motivated causal-metaphysical assumptions. We find that the LF inequalities emerge from this causal structure even when one allows the latent causes of observed events to admit post-quantum descriptions, such as in a generalized probabilistic theory or in an even more exotic theory. We further prove that no nonclassical causal model can explain violations of LF inequalities without violating the No Fine-Tuning principle. Finally, we note that these obstacles cannot be overcome even if one appeals to cyclic causal models, and we discuss potential directions for further extensions of the causal modeling framework.

quant-ph↗