John Selby

Imperial College London | Imperial · Department of Physics

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 a...

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 t...

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 tomograph...

Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Castro-Ruiz et al. pursues this using the process-matrix formalism, together with a definition of the possible dynamics of such process matrices, and...

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 noncontextuali...

Generalised contextuality is a well-motivated 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 reso...

In this work we show that the set of nonsignaling resources of a locally tomographic generalized 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...

It is useful to have a criterion for when the predictions of an operational theory should be considered classically explainable. Here we take the criterion to be that the theory admits of a generalized-noncontextual ontological model. Existing works on generalized noncontextuality have focused on experimental scenarios having a simple structure: ty...

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 conc...

Deriving quantum mechanics from information-theoretic postulates is a recent research direction taken, in part, with the view of finding a beyond-quantum theory; once the postulates are clear, we can consider modifications to them. A key postulate is the purification postulate, which we propose to replace by a more generally applicable postulate th...

When gravity is sourced by a quantum system, there is tension between its role as the mediator of a fundamental interaction, which is expected to acquire nonclassical features, and its role in determining the properties of spacetime, which is inherently classical. Fundamentally, this tension should result in breaking one of the fundamental principl...

Generalized contextuality is a resource for a wide range of communication and information processing protocols. However, contextuality is not possible without coherence, and so can be destroyed by dephasing noise. Here, we explore the robustness of contextuality to partially dephasing noise in a scenario related to state discrimination (for which c...

How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the correlations that physical theories may feature when restricted by some particular constraints on their measuremen...

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 th...

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 particu...

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 cla...

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 con...

When gravity is sourced by a quantum system, there is tension between its role as the mediator of a fundamental interaction, which is expected to acquire nonclassical features, and its role in determining the properties of spacetime, which is inherently classical. Fundamentally, this tension should result in breaking one of the fundamental principl...

Generalized contextuality is a resource for a wide range of communication and information processing protocols. However, contextuality is not possible without coherence, and so can be destroyed by dephasing noise. Here, we explore the robustness of contextuality to partially dephasing noise in a scenario related to state discrimination (for which c...

There is a stark tension among different formulations of quantum theory in that some are fundamentally time-symmetric and others are radically time-asymmetric. This tension is crisply captured when thinking of physical theories as theories of processes. We review process theories and their diagrammatic representation, and show how quantum theory ca...

We give a complete characterization of the (non)classicality of all stabilizer subtheories. First, we prove that there is a unique nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory in all odd dimensions, namely Gross’s discrete Wigner function. This representation is equivalent to Spekkens’ epistemically...

Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled solely due to the...

We present the first instance where post-quantum steering is a stronger-than-quantum resource for information processing – remote state preparation. In addition, we show that the phenomenon of post-quantum steering is not just a mere mathematical curiosity allowed by the no-signalling principle, but it may arise within compositional theories beyond...

The gold standard for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here provide an open-source linear program for testing whether or not any given prepare-measure experiment is classically-explainable in this sense. The input to the program is simply an ar...

Non-signalling quantum channels -- relevant in, e.g., the study of Bell and Einstein-Podolsky-Rosen scenarios -- may be simulated via affine combinations of local operations in bipartite scenarios. Moreover, when these channels correspond to stochastic maps between classical variables, such simulation is possible even in multipartite scenarios. The...

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 particu...

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 and more perm...

To make precise the sense in which the operational predictions of quantum theory conflict with a classical worldview, it is necessary to articulate a notion of classicality within an operational framework. A widely applicable notion of classicality of this sort is whether or not the predictions of a given operational theory can be explained by a ge...

We present the first instance where post-quantum steering is a stronger-than-quantum resource for information processing -- remote state preparation. In addition, we show that the phenomenon of post-quantum steering is not just a mere mathematical curiosity allowed by the no-signalling principle, but it may arise within compositional theories beyon...

We prove that there is a unique nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory in odd dimensions, namely Gross' discrete Wigner function. This representation is equivalent to Spekkens' epistemically restricted toy theory, which is consequently singled out as the unique noncontextual ontological model...

Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled due to solely the...

Coin flipping is a fundamental cryptographic task where spatially separated Alice and Bob wish to generate a fair coin flip over a communication channel. It is known that ideal coin flipping is impossible in both classical and quantum theory. In this work, we give a short proof that it is also impossible in generalized probabilistic theories under...

Quantum coherence is one of the most important resources in quantum information theory. Indeed, preventing the loss of coherence is one of the most important technical challenges obstructing the development of large-scale quantum computers. Recently, there has been substantial progress in developing mathematical resource theories of coherence, pavi...

How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the correlations that physical theories may feature when restricted by some particular constraints on their measuremen...

Using a process-theoretic formalism, we introduce the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of how these interact. Recasting the notions of operational and realist theories in this mold clarifies what a rea...

Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Ref. [Phys. Rev. X 8.1 (2018): 011047] pursues this using the process matrix formalism, together with a definition of the possible dynamics of such p...

It is useful to have a criterion for when the predictions of an operational theory should be considered classically explainable. Here we take the criterion to be that the theory admits of a generalized-noncontextual ontological model. Existing works on generalized noncontextuality have focused on experimental scenarios having a simple structure, ty...

One of the most well-motivated and widely applicable notions of classicality for an operational theory is explainability by a generalized-noncontextual ontological model. We here explore what notion of classicality this implies for the generalized probabilistic theory (GPT) that arises from a given operational theory, focusing on prepare-and-measur...

Quantum coherence is one of the most important resources in quantum information theory. Indeed, preventing the loss of coherence is one of the most important technical challenges obstructing the development of large-scale quantum computers. Recently, there has been substantial progress in developing mathematical resource theories of coherence, pavi...

Coin-flipping is a fundamental cryptographic task where a spatially separated Alice and Bob wish to generate a fair coin-flip over a communication channel. It is known that ideal coin-flipping is impossible in both classical and quantum theory. In this work, we give a short proof that it is also impossible in generalized probabilistic theories unde...

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a well-defined oracle model. Indee...

Quantum theory is the most experimentally verified physical theory in the history of science. Yet it may be the case that quantum theory is only an effective description of the world, in the same way that classical physics is an effective description of the quantum world. In this work we ask whether there can exist an operationally-defined theory s...

We discuss the possibility of creating money that is physically impossible to counterfeit. Of course, "physically impossible" is dependent on the theory that is a faithful description of nature. Currently there are several proposals for quantum money which have their security based on the validity of quantum mechanics. In this work, we examine Wies...

We discuss the possibility of creating money that is physically impossible to counterfeit. Of course, "physically impossible" is dependent on the theory that is a faithful description of nature. Currently there are several proposals for quantum money which have their security based on the validity of quantum mechanics. In this work, we examine Wies...

A reconstruction of quantum theory refers to both a mathematical and a conceptual paradigm that allows one to derive the usual formulation of quantum theory from a set of primitive assumptions. The motivation for doing so is a discomfort with the usual formulation of quantum theory, a discomfort that started with its originator John von Neumann. W...

We present a reconstruction of finite-dimensional quantum theory where all of the postulates are stated in diagrammatic terms, making them intuitive. Equivalently, they are stated in category-theoretic terms, making them mathematically appealing. Again equivalently, they are stated in process-theoretic terms, establishing that the conceptual backbo...

We consider a very general class of theories, process theories, which capture the underlying structure common to most theories of physics as we understand them today (be they established, toy or speculative theories). Amongst these theories, we will be focusing on those which are `causal', in the sense that they are intrinsically compatible with th...

Bit-commitment is a fundamental cryptographic task where Alice wishes to commit to Bob a bit in such a way that it cannot be changed while simultaneously being hidden from Bob. It is known that ideal bit-commitment is impossible using quantum theory. In this work, we show that it is also impossible in generalised probabilistic theories (GPTs) under...

Bit-commitment is a fundamental cryptographic task, in which Alice commits a bit to Bob such that she cannot later change the value of the bit, while, simultaneously, the bit is hidden from Bob. It is known that ideal bit-commitment is impossible within quantum theory. In this work, we show that it is also impossible in generalised probabilistic th...

We show that the physical principle, “the adjoint associates to each state a ‘test’ for that state”, fully characterises the Hermitian adjoint for pure quantum theory, therefore providing the adjoint with operational meaning beyond its standard mathematical definition. Moreover, we demonstrate that for general process theories, which all admit a di...

One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein’s so called “spooky action at a distance.” These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have e...

One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance". These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have e...

As first noted by Rafael Sorkin, there is a limit to quantum interference. The interference pattern formed in a multi-slit experiment is a function of the interference patterns formed between pairs of slits; there are no genuinely new features resulting from considering three slits instead of two. Sorkin has introduced a hierarchy of mathematically...

As first noted by Rafael Sorkin, there is a limit to quantum interference. The interference pattern formed in a multi-slit experiment is a function of the interference patterns formed between pairs of slits, there are no genuinely new features resulting from considering three slits instead of two. Sorkin has introduced a hierarchy of mathematically...

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying three natural physical principles possess a well-defined oracle model. Inde...

We introduce the notion of a leak for general process theories, and identify quantum theory as a theory with minimal leakage, while classical theory has maximal leakage. We provide a construction that adjoins leaks to theories, an instance of which describes the emergence of classical theory by adjoining decoherence-leaks to quantum theory. Finally...

Mixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two `roads to classicality' coincide. This is indeed the case for (finite-dimensional) quantum theory, where each construction yields the category of C*-algebr...

To date, there has been no experimental evidence that invalidates quantum theory. Yet it may only be an effective description of the world, in the same way that classical physics is an effective description of the quantum world. We ask whether there exists an operationally-defined theory superseding quantum theory, but which reduces to it via a dec...

Quantum interference lies at the heart of several quantum computational speed-ups and provides a striking example of a phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a three slit experiment. In this set-up, the interference pattern can be written in terms of the two and one slit patterns obtained b...

One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance". These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of which physical principles give rise to entanglement. Why does quantum theory h...

Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key resource behind this computational speed-up. However there is a limit to this interference, at most pairs of pat...

We show that the physical principle "the adjoint associates to each state a `test' for that state" fully characterises the Hermitian adjoint for pure quantum theory, therefore providing the adjoint with operational meaning beyond its standard mathematical definition. Also, we show that for general process theories, which all admit a diagrammatic re...

Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key resource behind this computational speed-up. However there is a limit to this interference, at most pairs of pat...

The advent of quantum computing has challenged classical conceptions of which problems are efficiently solvable in our physical world. This motivates the general study of how physical principles bound computational power. In this paper we show that some of the essential machinery of quantum computation—namely reversible controlled transformations a...

The advent of quantum computing has challenged classical conceptions of which problems are efficiently solvable in our physical world. This motivates the general study of how physical principles bound computational power. A major roadblock to such a study is that quantum computation is phrased in the language of Hilbert spaces, which lacks direct o...