arXiv subjects

David Schmid

Publications and source records attributed to David Schmid.

At least 19 recordsLinked to original sources

arXiv2026

Tomographically-nonlocal entanglement

Entanglement is a central and subtle feature of quantum theory, whose structure and operational behavior can change dramatically when additional physical constraints, such as symmetries or superselection rules, are imposed. Such constraints can give rise to striking and counter-intuitive phenomena, including local broadcasting of entangled states and failures of entanglement monogamy. These effects naturally arise in tomographically nonlocal theories (like real quantum theory, twirled worlds, or fermionic quantum theory), where composite systems possess holistic degrees of freedom that are inaccessible to local measurements. In this work, we study entanglement in such theories within the framework of generalized probabilistic theories. We show that the failure of tomographic locality leads to two qualitatively distinct forms of entanglement, which we term $\textit{tomographically-local}$ entanglement and $\textit{tomographically-nonlocal}$ entanglement. We analyze the operational consequences of this distinction, proving that tomographically-nonlocal entanglement is useless for Bell nonlocality, steering, and teleportation, but sufficient for dense coding and perfectly secure data hiding. This framework clarifies the origin of several previously puzzling features of entanglement that arise when tomographic locality fails, as can happen even in quantum theory when one considers fermions or fundamental superselection rules.

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arXiv2025

Quantum oracles give an advantage for identifying classical counterfactuals

We show that quantum oracles provide an advantage over classical oracles for answering classical counterfactual questions in causal models, or equivalently, for identifying unknown causal parameters such as distributions over functional dependences. In structural causal models with discrete classical variables, observational data and even ideal interventions generally fail to answer all counterfactual questions, since different causal parameters can reproduce the same observational and interventional data while disagreeing on counterfactuals. Using a simple binary example, we demonstrate that if the classical variables of interest are encoded in quantum systems and the causal dependence among them is encoded in a quantum oracle, coherently querying the oracle enables the identification of all causal parameters -- hence all classical counterfactuals. We generalize this to arbitrary finite cardinalities and prove that coherent probing 1) allows the identification of all two-way joint counterfactuals p(Y_x=y, Y_{x'}=y'), which is not possible with any number of queries to a classical oracle, and 2) provides tighter bounds on higher-order multi-way counterfactuals than with a classical oracle. This work can also be viewed as an extension to traditional quantum oracle problems such as Deutsch--Jozsa to identifying more causal parameters beyond just, e.g., whether a function is constant or balanced. Finally, we raise the question of whether this quantum advantage relies on uniquely non-classical features like contextuality. We provide some evidence against this by showing that in the binary case, oracles in some classically-explainable theories like Spekkens' toy theory also give rise to a counterfactual identifiability advantage over strictly classical oracles.

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arXiv2025

The resource theory of causal influence and knowledge of causal influence

Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. In this work, we develop a resource-theoretic framework to do so. Here, we focus on the simplest nontrivial setting -- two variables that are causally ordered, meaning that the first has the potential to influence the second, without hidden confounding. First, we introduce the resource theory that directly quantifies causal influence of a functional dependence in this setting and show that the problem of deciding convertibility of resources and identifying a complete set of monotones has a relatively straightforward solution. Following this, we introduce the resource theory that arises naturally when one has uncertainty about the functional dependence. We describe a linear program for deciding the question of whether one resource (i.e., state of knowledge about the functional dependence) can be converted to another. Then, we focus on the case where the variables are binary. In this case, we identify a triple of monotones that are complete in the sense that they capture the partial order over the set of all resources, and we provide an interpretation of each.

math.ST↗

arXiv2025

A contextual advantage for conclusive exclusion: repurposing the Pusey-Barrett-Rudolph construction

The task of conclusive exclusion for a set of quantum states is to find a measurement such that for each state in the set, there is an outcome that allows one to conclude with certainty that the state in question was not prepared. Defining classicality of statistics as realizability by a generalized-noncontextual ontological model, we show that there is a quantum-over-classical advantage for how well one can achieve conclusive exclusion. This is achieved in an experimental scenario motivated by the construction appearing in the Pusey-Barrett-Rudolph theorem. We derive noise-robust noncontextuality inequalities bounding the conclusiveness of exclusion, and describe a quantum violation of these. Finally, we show that this bound also constitutes a classical causal compatibility inequality within the bilocality scenario, and that its violation in quantum theory yields a novel possibilistic proof of a quantum-classical gap in that scenario.

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arXiv2025

Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory

We construct an ontological model for the theory known as bilocal classical theory doi.org/10.1103/PhysRevA.102.052216. To our knowledge, this is only the second time that an ontological model has been constructed for an entire theory, rather than just for some particular scenarios within a theory. This result refutes a conjecture from doi.org/10.1103/PhysRevA.102.052216 which suggested that there might be no local-realist ontological model for bilocal classical theory. Moreover, it is the first time that an ontological model has been constructed for a theory that fails to be locally tomographic, showing that the assumption of local tomography underpinning the structure theorem in doi.org/10.22331/q-2024-03-14-1283 is a genuine limitation of the theorem. This demonstrates that in general there is no tension between failures of local tomography and classical explainability (i.e., generalised noncontextuality). In fact, bilocal classical theory is in many ways more simply understood via the underlying ontological model than it is within its original formulation (much as how odd-dimensional stabiliser subtheories can be more simply understood via Spekkens' toy theory). Furthermore, this result naturally leads to the question, does every locally-classical theory admit of an ontological model? By constructing a concrete counterexample, we show that this is not the case. Our findings demonstrate that there is no straightforward relationship between theories being locally-classical, and them being classically-explainable. This shows that the fundamental status of compositional properties (such as local tomography) is not a technical side-issue, but a central and unavoidable question for a coherent understanding even of classicality itself.

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arXiv2025

Typicality of Contextuality

Identifying when observed statistics cannot be explained by any reasonable classical model is a central problem in quantum foundations. A principled and universally applicable approach to defining and identifying nonclassicality is given by the notion of generalized noncontextuality. Here, we study the typicality of contextuality -- namely, the likelihood that randomly chosen quantum preparations and measurements produce nonclassical statistics. Using numerical linear programs to test for the existence of a generalized-noncontextual model, we find that contextuality is fairly common: even in experiments with only a modest number of random preparations and measurements, contextuality arises with probability over 99%. We also show that while typicality of contextuality decreases as the purity (sharpness) of the preparations (measurements) decreases, this dependence is not especially pronounced, so contextuality is fairly typical even in settings with realistic noise. Finally, we show that although nonzero contextuality is quite typical, quantitatively high degrees of contextuality are not as typical, and so large quantum advantages (like for parity-oblivious multiplexing, which we take as a case study) are not as typical. We provide an open-source toolbox that outputs the typicality of contextuality as a function of tunable parameters (such as lower and upper bounds on purity and other constraints on states and measurements). This toolbox can inform the design of experiments that achieve the desired typicality of contextuality for specified experimental constraints.

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arXiv2025

A structure theorem for complex-valued quasiprobability representations of physical theories

Quasiprobability representations are well-established tools in quantum information science, with applications ranging from the classical simulability of quantum computation to quantum process tomography, quantum error correction, and quantum sensing. While traditional quasiprobability representations typically employ real-valued distributions, recent developments highlight the usefulness of complex-valued ones -- most notably, via the family of Kirkwood--Dirac quasiprobability distributions. Building on the framework of Schmid et al. [Quantum 8, 1283 (2024)], we extend the analysis to encompass complex-valued quasiprobability representations that need not preserve the identity channel. Additionally, we also extend previous results to consider mappings towards infinite-dimensional spaces. We show that, for each system, every such representation can be expressed as the composition of two maps that are completely characterized by their action on states and on the identity (equivalently, on effects) for that system. Our results apply to all complex-valued quasiprobability representations of any finite-dimensional, tomographically-local generalized probabilistic theory, with finite-dimensional quantum theory serving as a paradigmatic example. In the quantum case, the maps' action on states and effects corresponds to choices of frames and dual frames for the representation. This work offers a unified mathematical framework for analyzing complex-valued quasiprobability representations in generalized probabilistic theories.

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arXiv2025

Entanglement certification using noncontextuality inequalities

By combining the assumptions of Bell locality with those of generalized noncontextuality, we define classes of noncontextuality inequalities for correlations arising in a bipartite Bell circuit. These classes are distinguished by which subsets of the full set of operational identities are taken as input to the principle of noncontextuality; certain natural subsets form a hierarchy that provides a new way of understanding and classifying quantum correlations, including entanglement, steering, and nonlocality. Each level of this hierarchy gives rise to a corresponding class of noncontextuality inequalities whose violation witnesses one of these forms of bipartite quantum resourcefulness, thereby yielding different sufficient conditions for entanglement. The resulting entanglement certification paradigm requires no prior characterization of the measurements, is independent of tomographic gauge freedom, and can certify any entangled state without auxiliary entangled sources. To illustrate its power, we show that noncontextuality inequalities can certify entanglement for families of two-qubit isotropic states for which Bell or steering inequalities are known to fail. We also show that, compared with the Bell test, this approach certifies a much larger fraction of entangled states, while the associated membership problem is more tractable. On the experimental side, we describe techniques to ensure nontrivial operational identities in the presence of noisy and imperfect implementations. We also identify the key assumption under which these techniques are valid, namely, a particular notion of tomographic completeness, which ensures that the operational identities are gauge-independent. Finally, we provide an experimental demonstration of the superior performance of this entanglement certification technique using polarization-entangled photons.

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arXiv2025

On whether quantum theory needs complex numbers: the foil theories perspective

Recent work by Renou et al. (2021) has led to some controversy concerning the question of whether quantum theory requires complex numbers for its formulation. We promote the view that the main result of that work is best understood not as a claim about the relative merits of different representations of quantum theory, but rather as a claim about the possibility of experimentally adjudicating between standard quantum theory and an alternative theory -- a foil theory -- known as real-amplitude quantum theory (RQT). In particular, the claim is that this adjudication can be achieved given only an assumption about the causal structure of the experiment. Here, we aim to shed some light on why this is possible, by reconceptualizing the comparison of the two theories as an instance of a broader class of such theory comparisons. By recasting RQT as the subtheory of quantum theory that arises by symmetrizing with respect to the collective action of a time-reversal symmetry, we can compare it to other subtheories that arise by symmetrization, but for different symmetries. If the symmetry has a unitary representation, the resulting foil theory is termed a twirled quantum world, and if it does not (as is the case in RQT), the resulting foil theory is termed a swirled quantum world. We show that, in contrast to RQT, there is no possibility of distinguishing any twirled quantum world from quantum theory given only an assumption about causal structure. We also define analogues of twirling and swirling for an arbitrary generalized probabilistic theory and identify certain necessary conditions on a causal structure for it to be able to support a causal compatibility gap between the theory and its symmetrized version. We draw out the implications of these analyses for the question of how a lack of a shared reference frame state features into the possibility of such a gap.

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arXiv2025

Copenhagenish interpretations of quantum mechanics

We define a class of Copenhagenish interpretations encompassing modern interpretations that follow the Copenhagen spirit. These interpretations are characterized by four postulates: Observers Observe, Universality, Anti-$\psi$-ontology, and Completeness. We explain why such interpretations are not equivalent to the textbook (or orthodox) interpretation, nor to the view that one should shut up and calculate, nor to strict operationalism. We then discuss what lessons are implied for Copenhagenish interpretations by the measurement problem, the Wigner's friend thought experiment, and the simple variants of the Wigner's friend thought experiment that we term Wigner's enemy, stalkee, and penpal. In particular, we discuss how Copenhagenish interpretations give multiple distinct descriptions of each experiment, where these descriptions are each individually true, yet cannot be combined into any single description. To make such interpretations consistent, then, one requires epistemological constraints forbidding certain perspectives from being combined. We discuss these constraints, their motivations, and some of the challenges they introduce.

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arXiv2025

Quantifiers and witnesses for the nonclassicality of measurements and of states

In recent work Phys. Rev. X 16, 021050, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, and sets thereof. This notion is derived from the principle of generalized noncontextuality, but in a novel manner that applies to individual processes rather than full experiments or theories. In the present work, we develop semidefinite-programming-based certificates and witnesses for the nonclassicality of states, sources, measurements, and sets thereof. These theory-dependent methods complement theory-independent approaches based on noncontextuality inequalities. We demonstrate the framework through a variety of explicit examples.

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arXiv2025

Reassessing the boundary between classical and nonclassical for individual quantum processes

There is a received wisdom about where to draw the boundary between classical and nonclassical for various types of quantum processes. For multipartite states, it is the divide between separable and entangled; for channels, the divide between entanglement-breaking and not; for sets of measurements, the divide between compatible and incompatible; for assemblages, the divide between steerable and unsteerable. However, these choices have not been motivated by any unified notion of what it means to be classically explainable. One well-motivated notion of classical explainability is the one based on generalized noncontextuality: a set of circuits is classically explainable if a generalized-noncontextual ontological model can realize the statistics they generate. In this work, we show that this notion can be leveraged to define a classical-nonclassical divide for individual quantum processes of arbitrary type. We begin the task of characterizing where the classical-nonclassical divide lies according to this proposal for a variety of different types of processes. In particular, we show that all of the following are judged to be nonclassical: every entangled state, every set of incompatible measurements, every non-entanglement-breaking channel, and every steerable assemblage. Our proposal differs from the received wisdom, however, insofar as it also judges certain subsets of the complementary classes to be nonclassical, including certain separable states, compatible sets of measurements, entanglement-breaking channels, and unsteerable assemblages. Finally, we prove structure theorems characterizing the classical-nonclassical divide based on whether a process admits of a specific type of frame representation.

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arXiv2025

Noncontextual ontological models of operational probabilistic theories

An experiment or theory is classically explainable if it can be reproduced by some noncontextual ontological model. In this work, we adapt the notion of ontological models and generalized noncontextuality so it applies to the framework of operational probabilistic theories (OPTs). A defining feature of quotiented OPTs, which sets them apart from the closely related framework of generalized probabilistic theories (GPTs), is their explicit specification of the structure of instruments, these being generalizations of $\textit{quantum instruments}$ (including nondestructive measurements); in particular, one needs to explicitly declare which collections of transformations constitute a valid instrument. We are particularly interested in strongly causal OPTs, in which the choice of a future instrument can be conditioned on a past measurement outcome. This instrument structure might seem to permit the possibility of a contextual kind of ontological representation, where the representation of a given transformation depends on which instrument it is considered a part of. However, we prove that this is not possible by showing that for strongly causal quotiented OPTs the structure of instruments does $\textit{not}$ allow for such a contextual ontological representation. It follows that ontological representations of strongly causal quotiented OPTs are entirely determined by their action on individual transformations, with no dependence on the structure of instruments.

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arXiv2024

Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs

It is commonly believed that failures of tomographic completeness undermine assessments of nonclassicality in noncontextuality experiments. In this work, we study how such failures can indeed lead to mistaken assessments of nonclassicality. We then show that proofs of the failure of noncontextuality are robust to a very broad class of failures of tomographic completeness, including the kinds of failures that are likely to occur in real experiments. We do so by showing that such proofs actually rely on a much weaker assumption that we term relative tomographic completeness: namely, that one's experimental procedures are tomographic for each other. Thus, the failure of noncontextuality can be established even with coarse-grained, effective, emergent, or virtual degrees of freedom. This also implies that the existence of a deeper theory of nature (beyond that being probed in one's experiment) does not in and of itself pose any challenge to proofs of nonclassicality. To prove these results, we first introduce a number of useful new concepts within the framework of generalized probabilistic theories (GPTs). Most notably, we introduce the notion of a GPT subsystem, generalizing a range of preexisting notions of subsystems (including those arising from tensor products, direct sums, decoherence processes, virtual encodings, and more). We also introduce the notion of a shadow of a GPT fragment, which captures the information lost when one's states and effects are unknowingly not tomographic for one another.

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arXiv2024

Connecting extended Wigner's friend arguments and noncontextuality

The Local Friendliness argument is an extended Wigner's friend no-go theorem that provides strong constraints on the nature of reality -- stronger even than those imposed by Bell's theorem or by noncontextuality arguments. In this work, we prove a variety of connections between Local Friendliness scenarios and Kochen-Specker noncontextuality. Specifically, we first show how one can derive new Local Friendliness inequalities using known tools and results from the literature on Kochen-Specker noncontextuality. In doing so, we provide a new derivation for some of the facets of the Local Friendliness polytope, and we prove that this polytope is equal to the Bell polytope in a wide range of extended Wigner's friend scenarios with multipartite agents and sequential measurements. We then show how any possibilistic Kochen-Specker argument can be mathematically translated into a related proof of the Local Friendliness no-go theorem. In particular, we construct a novel kind of Local Friendliness scenario where a friend implements several compatible measurements (or joint measurements of these) in between the superobserver's operations on them. We illustrate this with the well-known 5-cycle and Peres-Mermin contextuality arguments.

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arXiv2024

Symmetry-induced failures of tomographic locality: Constructing foil theories by twirling

Tomographic locality is a principle commonly used in the program of finding axioms that pick out quantum theory within the landscape of possible theories. The principle asserts the sufficiency of local measurements for achieving a tomographic characterization of any bipartite state. In this work, we explore the meaning of the principle of tomographic locality by developing a simple scheme for generating a wide variety of theories that violate the principle. In this scheme, one starts with a tomographically local theory -- which can be classical, quantum or post-quantum -- and a physical symmetry, and one restricts the processes in the theory to all and only those that are covariant with respect to the collective action of that symmetry. We refer to the resulting theories as twirled worlds. We show that failures of tomographic locality are ubiquitous in twirled worlds. From the possibility of such failures in classical twirled worlds, we argue that the failure of tomographic locality (i.e., tomographic nonlocality) does not imply ontological holism. Our results also demonstrate the need for researchers seeking to axiomatize quantum theory to take a stand on the question of whether there are superselection rules that have a fundamental status.

quant-ph↗

arXiv2024

Noncontextuality inequalities for prepare-transform-measure scenarios

We provide the first systematic technique for deriving witnesses of contextuality in prepare-transform-measure scenarios. More specifically, we show how linear quantifier elimination can be used to compute a polytope of correlations consistent with generalized noncontextuality in such scenarios. This polytope is specified as a set of noncontextuality inequalities that are necessary and sufficient conditions for observed data in the scenario to admit of a classical explanation relative to any linear operational identities, if one ignores some constraints from diagram preservation. While including these latter constraints generally leads to tighter inequalities, it seems that nonlinear quantifier elimination would be required to systematically include them. We also provide a linear program which can certify the nonclassicality of a set of numerical data arising in a prepare-transform-measure experiment. We apply our results to get a robust noncontextuality inequality for transformations that can be violated within the stabilizer subtheory. Finally, we give a simple algorithm for computing all the linear operational identities holding among a given set of states, of transformations, or of measurements.

quant-ph↗

arXiv2024

Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)

Kirkwood-Dirac representations of quantum states are increasingly finding use in many areas within quantum theory. Usually, representations of this sort are only applied to provide a representation of quantum states (as complex functions over some set). We show how standard Kirkwood-Dirac representations can be extended to a fully compositional representation of all of quantum theory (including channels, measurements and so on), and prove that this extension satisfies the essential features of functoriality (namely, that the representation commutes with composition of channels), linearity, and quasistochasticity. Interestingly, the representation of a POVM element is uniquely picked out to be the collection of weak values for it relative to the bases defining the representation. We then prove that if one can find any Kirkwood-Dirac representation that is everywhere real and nonnegative for a given experimental scenario or fragment of quantum theory, then the scenario or fragment is consistent with the principle of generalized noncontextuality, a key notion of classicality in quantum foundations. We also show that the converse does not hold: even if one verifies that all Kirkwood-Dirac representations (as defined herein) of an experiment require negativity or imaginarity, one cannot generally conclude that the experiment witnesses contextuality.

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