Testing quantum mechanics against alternative theories must be done in a way that does not make assumptions about the validity of any particular theory, in particular, without presuming the correctness of quantum theory. Here, the authors set bounds on possible deviations from quantum theory using the formalism of Generalized Probabilistic Theories by experimentally probing a three-level system consisting of a photon shared among three modes. They find no evidence for the breakdown of quantum theory.
Testing quantum mechanics against alternative theories must be done in a way that does not make assumptions about the validity of any particular theory, in particular, without presuming the correctness of quantum theory. Here, the authors set bounds on possible deviations from quantum theory using the formalism of Generalized Probabilistic Theories by experimentally probing a three-level system consisting of a photon shared among three modes. They find no evidence for the breakdown of quantum theory.
Many experiments in the field of quantum foundations seek to adjudicate between quantum theory and speculative alternatives to it.This requires one to analyze the experimental data in a manner that does not presume the correctness of the quantum formalism.The mathematical framework of generalized probabilistic theories (GPTs) provides a means of doing so.We present a scheme for determining which GPTs are consistent with a given set of experimental data.It proceeds by performing tomography on the preparations and measurements in a self-consistent manner, i.e., without presuming a prior characterization of either.We illustrate the scheme by analyzing experimental data for a large set of preparations and measurements on the polarization degree of freedom of a single photon.We first test various hypotheses for the dimension of the GPT vector space for this degree of freedom.Our analysis identifies the most plausible hypothesis to be dimension 4, which is the value predicted by quantum theory.Under this hypothesis, we can draw the following additional conclusions from our scheme: (i) that the smallest and largest GPT state spaces that could describe photon polarization are a pair of polytopes, each approximating the shape of the Bloch sphere and having a volume ratio of 0.977 ± 0.001, which provides a quantitative bound on the scope for deviations from the state and effect spaces predicted by quantum theory, and (ii) that the maximal violation of the Clauser, Horne, Shimony, and Holt inequality can be at most 1.3% ± 0.1 greater than the maximum violation allowed by quantum theory, and the maximal violation of a particular inequality for universal noncontextuality can not differ from the quantum prediction by more than this factor on either side.The only possibility for a greater deviation from the quantum state and effect spaces or for greater degrees of supraquantum nonlocality or contextuality, according to our analysis, is if a future experiment (perhaps following the scheme developed here) discovers that additional dimensions of GPT vector space are required to describe photon polarization, in excess of the four dimensions predicted by quantum theory to be adequate to the task.
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.
To date, quantum theory is the most successful physical theory that has been discovered. However, there is still the possibility that an inconsistency between experimental observations and the predictions of quantum theory may one day be found, thus prompting the replacement of quantum theory with a superior, post-quantum theory. To narrow down the scope of possibilities for the true theory that describes nature, one can perform experiments that falsify other physical theories, by demonstrating an incompatibility between experimental observations and the predictions of these theories. This thesis details two such experiments. First we provide relevant background information, beginning with a review of experimental quantum optics. Next, we review noncontextual ontological theories and discuss requirements for experimental tests of such theories. Finally, we discuss the framework of generalised probabilistic theories before introducing the two experiments. \n \n \nThe first experiment is a test of noncontextual ontological (or hidden-variable) models of nature. An ontological model of a physical theory is one in which systems have preexisting properties, and a noncontextual ontological model is one in which systems that are indistinguishable experimentally are represented identically in the model. Physical theories that cannot be represented by a noncontextual ontological model are said to be nonclassical; quantum theory is an example of such a physical theory that is nonclassical in this sense. Prior to this thesis, experimental tests of the assumption of noncontextuality had assumed that the experiments were free of both systematic and statistical errors, which is not justifiable for any experiment. We introduce new analytical techniques that allow us to avoid making these assumptions, and perform an experiment with single photons that, with high confidence, rules out the possibility of describing nature with a noncontextual ontological model. \n \n \nThe second experiment is a demonstration of self-consistent state and measurement tomography in the framework of generalised probabilistic theories (GPTs). The GPT framework is a very general, operationally-motivated framework for describing a physical theory in terms of the observable events predicted by the theory. We develop a technique for inferring the GPT description of a set of states and measurements directly from experimental data. By analysing our data in this general framework, we are able to test various candidate physical theories of nature. We perform an experiment with single photons, and quantify the size of possible variations between quantum theory and the true physical theory that describes nature.
The principle of tomographic locality states that the operational state of a multipartite system can be fully characterized by the statistics obtained from measurements that are local to the individual subsystems. This property holds in quantum theory and features prominently in axiomatic reconstructions of the theory, where it serves to rule out a wide class of alternatives. For instance, quantum theory with Hilbert spaces defined over the real field (rather than the complex field) is an example of a theory that is ruled out in this fashion. Given its foundational importance, it is worthwhile to subject this principle to a direct experimental test. Specifically, we consider an experiment on the polarization degrees of freedom of a pair of photonic modes in a prepare-and-measure scenario and analyze the resulting data within the framework of generalized probabilistic theories. The signature of a failure of tomographic locality is that there are pairs of states on the bipartite system that can only be distinguished by the statistics they yield for non-separable measurements. In the full quantum setting, we find no evidence of a violation of tomographic locality. As a test of our analysis method, we also verify that if we restrict attention to those states and measurements that lie within the fragment described by quantum theory over the real field, then a clear signature of the failure of tomographic locality is observed.
Contextuality is a phenomenon at the heart of the quantum mechanical departure from classical behaviour, and has been recently identified as a resource in quantum computation. Experimental demonstration of contextuality is thus an important goal. The traditional form of contextuality -- as violation of a Kochen-Specker inequality -- requires a quantum system with at least three levels, and the status of the assumption of determinism used in deriving those inequalities has been controversial. By considering `unsharp' observables, Liang, Spekkens and Wiseman (LSW) derived an inequality for generalized noncontextual models that doesn't assume determinism, and applies already to a qubit. We experimentally implement the LSW test using the polarization states of a heralded single photon and three unsharp binary measurements. We violate the LSW inequality by more than 16 standard deviations, thus showing that our results cannot be reproduced by a noncontextual subset of quantum theory.
Self-testing usually refers to the task of taking a given set of observed correlations that are assumed to arise via a process that is accurately described by quantum theory, and trying to infer the quantum state and measurements. In other words it is concerned with the question of whether we can tell what quantum black-box devices are doing by looking only at their input-output behavior and is known to be possible in several cases. Here we introduce a more general question: is it possible to self-test a theory, and, in particular, quantum theory? More precisely, we ask whether within a particular causal structure there are tasks that can only be performed in theories that have the same correlations as quantum mechanics in any scenario. We present a candidate task for such a correlation self-test and analyze it in a range of generalized probabilistic theories (GPTs), showing that none of these perform better than quantum theory. A generalization of our results showing that all nonquantum GPTs are strictly inferior to quantum mechanics for this task would point to a new way to axiomatize quantum theory, and enable an experimental test that simultaneously rules out such GPTs.