arXiv subjects

John H. Selby

Publications and source records attributed to John H. Selby.

At least 19 recordsLinked to original sources

arXiv2026

Time symmetry in quantum theories and beyond

There exists a stark tension among different formulations of quantum theory as some are inherently time-symmetric while others are time-asymmetric. This tension is crisply captured when considering physical theories as theories of processes. We present the process theory of quantum physics, QPhys, which treats classical systems as internal to quantum theory. We provide three ways to incorporate time symmetry in QPhys. The first restricts the process theory of QPhys to one that satisfies an additional retrocausality constraint. The second is a novel approach, which extends the notions of causality and retrocausality to apply to systems along with processes. Utilizing this approach, we create a toy model for particle physics , where the causal and retrocausal systems correspond to particles and anti-particles respectively. The third approach extends QPhys to a supertheory that satisfies neither a causality nor a retrocausality constraint. To avoid unphysical predictions we modify either its composition rule or its processes.

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arXiv2026

Theory-agnostic nonclassicality certification in an integrated photonic circuit

Certifying nonclassicality without assuming any particular underlying physical theory constitutes both a foundational challenge and a requirement for device-independent protocols. Realizing such theory-independent certification in scalable architectures is essential for connecting fundamental tests with emerging quantum technologies. Integrated photonic circuits are a leading platform for scalable quantum information processing, motivating the development of rigorous methods to certify the nonclassical resources underpinning quantum advantage. In this paper, we report a theory-independent certification of generalized contextuality on a three-mode integrated photonic circuit. Our approach combines theory-agnostic tomography with simplex-embeddability certification---a framework that requires no assumptions about the underlying physical theory---and applies it to experimental data from a three-mode photonic circuit seeded by single photons. An independently constructed quantum model of the experiment provides a consistency check on the observed nonclassicality, without entering the certification as a theoretical assumption. The method rules out simplex-embeddability for our experimental data, providing robust, theory-independent evidence that our photonic circuit exhibits nonclassicality.

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arXiv2026

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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arXiv2026

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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arXiv2026

Polytopic Quantum Resource Theories: Geometry and Structures

Quantum resource theories provide a unifying framework to quantify, compare, and manipulate quantum resources under well-defined operational constraints. Here, we consider any resource theory where the set of free states can be expressed as a convex combination of a set of quantum states, referred to as extremal states and name them as polytopic quantum resource theories (PQRT). These include some of the most studied resource theories, such as coherence and magic. We formulate a novel tensorial representation of PQRTs that reveals the underlying geometry of these theories and provides insight into the origin of the resources. We further address a fundamental question in resource theories that when two theories should be regarded as physically equivalent, and to this purpose we introduce notions of homomorphism and isomorphism that compare both the structure of free states and the allowed transformations. Using the tools we develop, we find results revealing the geometrical and structural foundations of such theories. Interestingly, we find that all polytopic resource theories with a fixed number of pure extremal points are equivalent under a physical map, up to normalisation. Additionally, we introduce linearly independent polytopic resource theories (resource theory of ``basis-non-convexity''), where the set of extremal free states forms a basis of the quantum density operators. We further study the categorical structures of PQRTs beyond single systems.

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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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arXiv2026

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.

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arXiv2025

A decompositional framework for process theories in spacetime

There has been a recent surge of interest within the field of quantum foundations regarding incorporating ideas from general relativity and quantum gravity. However, many quantum information tools remain agnostic to the underlying spacetime. For instance, whenever we draw a quantum circuit the effective spacetime imposed by the connectivity of the physical qubits which will realize this circuit is not taken into account. In this work, we aim to address this limitation by extending the framework of process theories to include a background spacetime structure. We introduce the notion of process implementations, i.e., decompositions of a process. A process is then embeddable if and only if one of its implementations can be embedded in such a way that all the component processes are localized and all wires follow timelike paths. While conceptually simple, checking for embeddability is generally computationally intractable. We therefore work towards simplifying this problem as much as possible, identifying a canonical subset of implementations that determine both the embeddability of a process and the causal structures distinguishable at least in some process theory. Notably, we discover countably infinite ''zigzag'' causal structures beyond those typically considered. While these can be ignored in classical theory, they seem to be essential in quantum theory, as the quantum CNOT gate can be implemented by all zigzag structures but not in a standard causal structure, except in the trivial undecomposed way. These zigzags could be significant for quantum causal modeling and the study of novel quantum resources.

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arXiv2025

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.

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arXiv2025

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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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

Addressing some common objections to generalized noncontextuality

When should a given operational phenomenology be deemed to admit of a classical explanation? When it can be realized in a generalized-noncontextual ontological model. The case for answering the question in this fashion has been made in many previous works, and motivates research on the notion of generalized noncontextuality. Many criticisms and concerns have been raised, however, regarding the definition of this notion and of the possibility of testing it experimentally. In this work, we respond to some of the most common of these objections. One such objection is that the existence of a classical record of which laboratory procedure was actually performed in each run of an experiment implies that the operational equivalence relations that are a necessary ingredient of any proof of the failure of noncontextuality do not hold, and consequently that conclusions of nonclassicality based on these equivalences are mistaken. We explain why this concern in unfounded. Our response affords the opportunity for us to clarify certain facts about generalized noncontextuality, such as the possibility of having proofs of its failure based on a consideration of the subsystem structure of composite systems. Similarly, through our responses to each of the other objections, we elucidate some under-appreciated facts about the notion of generalized noncontextuality and experimental tests thereof.

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arXiv2025

Every non-signalling channel is common-cause realizable

In this work we show that the set of non-signalling resources of a locally-tomographic generalised probabilistic theory (GPT), such as quantum and classical theory, coincides with its set of GPT-common-cause realizable resources, where the common causes come from an associated GPT. From a causal perspective, this result provides a reason for, in the study of resource theories of common-cause processes, taking the non-signalling channels as the resources of the enveloping theory. This answers a critical open question in Ref.~\cite{schmid2020postquantum}. An immediate corollary of our result is that every non-signalling assemblage is realizable in a GPT, answering in the affirmative the question posed in Ref.~\cite{cavalcanti2022post}.

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arXiv2025

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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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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arXiv2025

Generalised Process Theories

Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories (SMCs). However, various generalizations, including time-neutral, higher-order, and enriched process theories, do not naturally conform to this structure. In this work, we propose an alternative formalization using operad algebras, motivated by recent results connecting SMCs to operadic structures, which captures a broader class of process theories. By leveraging the string-diagrammatic language, we provide an accessible yet rigorous formulation that unifies and extends traditional process-theoretic approaches. Our operadic framework not only recovers standard process theories as a special case but also enables new insights into quantum foundations and compositional structures. This work paves the way for further investigations into the algebraic and operational properties of generalised process theories within an operadic setting.

math.CT↗

arXiv2025

Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks

Generalised contextuality is the notion of nonclassicality powering up a myriad of quantum tasks, among which is the celebrated case of a two-party information processing task where classical information is compressed in a quantum channel, the parity-oblivious multiplexing (POM) task. The success rate is the standard quantifier of resourcefulness for this task, while robustness-based quantifiers are as operationally motivated and have known general properties. In this work, we leverage analytical and numerical tools to estimate robustness of contextuality in POM scenarios under different types of noise. We conclude that for the 3-to-1 case robustness of contextuality to depolarisation, as well as a minimisation of robustness of contextuality to dephasing over all bases, are good quantifiers for the nonclassical advantage of this scenario. Moreover, we obtain a general relation between robustness of contextuality to depolarisation and the success rate in any $n$-to-1 POM scenario and show how it can be used to bound the number of bits encoded in this task.

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arXiv2024

Indistinguishability in general probabilistic theories

The existence of indistinguishable quantum particles provides an explanation for various physical phenomena we observe in nature. We lay out a path for the study of indistinguishable particles in general probabilistic theories (GPTs) via two frameworks: the traditional GPT framework and the diagrammatic framework of process theories. In the first approach we define different types of indistinguishable particle by the orbits of symmetric states under transformations. In the diagrammatic approach, we find a decomposition of the symmetrised state space using two key constructions from category theory: the biproduct completion and the Karoubi envelope. In both cases for pairs of indistinguishable particles in quantum theory we recover bosons and fermions.

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