arXiv subjects

Theodoros Yianni

Publications and source records attributed to Theodoros Yianni.

4 recordsLinked to original sources

arXiv2026

Linear Algebra of Generalized Contextuality in All Prepare-Transform-Measure Scenarios

Generalized contextuality is a canonical distinguishing property of nonclassical generalized probabilistic theories, in particular quantum mechanics. Methods for certification and characterization of generalized contextuality of a given generalized probabilistic theory are well developed for prepare-measure and single-stage prepare-transform-measure scenarios. In a recent work [arXiv:2512.10000], a bottom-up, statistics-first linear-algebraic framework for contextuality in prepare-measure scenarios was introduced. We extend this approach to operational scenarios with sequential transformations with an arbitrary number of stages. We give a full decision procedure for contextuality of such scenarios within operational theories and analyze its computational complexity. In particular, our decision procedure has a complexity linearly exponential in the minimum generalized probabilistic theory (GPT) dimension, and polynomial in the number of procedures. We demonstrate our framework and approach through multiple examples, including Spekkens' toy theory and the 8-state single-qubit stabilizer theory. In particular, we construct an operational theory in which contextuality manifests itself only in the sequential structure of the transformations. Our findings thus shed new light on the significant role of compositional structures in the phenomenon of generalized contextuality.

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arXiv2026

A Unified Linear Algebraic Framework for Physical Models and Generalized Contextuality

We develop a bottom-up, statistics-first framework in which the full probabilistic content of an operational theory is encoded in its matrix of conditional outcome probabilities of events (COPE). Within this setting, five model classes (preGPTs, GPTs, quasiprobabilistic, ontological, and noncontextual ontological) are unified as constrained factorizations of the COPE matrix. We identify equirank factorizations as the structural core of GPTs and noncontextual ontological models and establish their relation to tomographic completeness. This yields a simple, model-agnostic criterion for noncontextuality: an operational theory admits a noncontextual ontological model if and only if its COPE matrix admits an equirank nonnegative matrix factorization (ENMF). Failure of the equirank condition in all ontological models therefore establishes contextuality. We operationalize rank separation via two complementary methods provided by the linear-algebraic framework. First, we use ENMF to interpret noncontextual ontological models as nested polytopes. This allows us to establish that the boxworld operational theory is ontologically contextual. Second, we apply techniques from discrete mathematics to derive a lower bound on the ontological dimensionality of COPE matrices exhibiting sparsity patterns, and use this bound to establish a new proof that a discrete version of qubit theory exhibits ontological contextuality. By reframing contextuality as a problem in matrix analysis, our work provides a unified structure for its systematic study and opens new avenues for exploring nonclassical resources.

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arXiv2026

Contextuality of all optimal quantum cloning

Quantum contextuality is a key nonclassical feature underlying advantages in quantum computation and communication. We introduce a new method to study contextuality in quantum information-processing tasks and protocols, relying solely on observed information-processing statistics. Building on the framework of Shahandeh, Yianni and Doosti in arXiv:2512.10000 and employing rank separation techniques, we prove that contextuality is the necessary resource in both phase-covariant and universal optimal quantum cloning, thereby establishing its role as a fundamental source of nonclassicality in all known optimal cloning scenarios and resolving an open problem on the connection between cloning and contextuality. As a second application, we demonstrate the power of our method by providing a new, streamlined proof of contextuality in minimum-error quantum state discrimination.

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arXiv2025

Complexity of Contextuality

Generalized contextuality is a hallmark of nonclassical theories like quantum mechanics. Yet, three fundamental computational problems concerning its decidability and complexity remain open. First, determining the complexity of deciding if a theory admits a noncontextual ontological model; Second, determining the complexity of deciding if such a model is possible for a specific dimension $k$; Third, efficiently computing the smallest such model when it exists, given that finding the smallest ontological model is NP-hard. We address the second problem by presenting an algorithm derived from a geometric formulation and its reduction to the intermediate simplex problem in computational geometry. We find that the complexity of deciding the existence of a noncontextual ontological model of dimension $k$ is at least exponential in the dimension of the theory and at most exponential in $k$. This, in turn, implies that computing the smallest noncontextual ontological model is inefficient in general. Finally, we demonstrate the fundamental difference between finding the smallest noncontextual ontological model and the smallest ontological model using an explicit example wherein the respective minimum ontic sizes are five and four.

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