Search Results (33)

This paper investigates quantum contextuality, a central nonclassical aspect of quantum mechanics, by employing the algebraic and topological structures of modular tensor categories. The analysis establishes that braid group representations constructed from modular categories, including the $SU{\left(2\right)}_k$ and Fibonacci anyon models, inherently produce state-dependent contextuality, as revealed by measurable violations of noncontextuality inequalities. The explicit construction of unitary representations on fusion spaces allows this paper to identify a direct structural correspondence between braiding operations and logical contextuality frameworks. The results offer a comprehensive topological framework to classify and quantify contextuality in low-dimensional quantum systems, thereby elucidating its role as a resource in topological quantum computation and advancing the interface between quantum algebra, topology, and quantum foundations. Full article

We give a variational characterization of the Born rule. For each measurement context, we project a quantum state ρ onto the corresponding abelian algebra by minimizing Umegaki relative entropy; Petz’s Pythagorean identity makes the dephased state the unique local minimizer, so the Born weights $p_C\left(i\right)=\mathrm{Tr}\left(\rho P_i\right)$ arise as a consequence, not an assumption. Globally, we measure contextuality by the minimum classical Kullback–Leibler distance from the bundle $\left\{p_C\left(\rho \right)\right\}$ to the noncontextual polytope, yielding a convex objective $\Phi \left(\rho \right)$. Thus, $\Phi \left(\rho \right)=0$ exactly when a sheaf-theoretic global section exists (noncontextuality), and $\Phi \left(\rho \right)>0$ otherwise; the closest noncontextual model is the classical I-projection of the Born bundle. Assuming finite dimension, full-rank states, and rank-1 projective contexts, the construction is unique and non-circular; it extends to degenerate PVMs and POVMs (via Naimark dilation) without change to the statements. Conceptually, the work unifies information-geometric projection, the presheaf view of contextuality, and categorical classical structure into a single optimization principle. Compared with Gleason-type, decision-theoretic, or envariance approaches, our scope is narrower but more explicit about contextuality and the relational, context-dependent status of quantum probabilities. Full article

We show that loophole-free Bell-type no-go theorems cannot be derived in theories involving local hidden fields. At the time of measurement, a contextuality loophole appears because each particle’s electromagnetic field interacts with the field of its respective apparatus, preventing the expression of the probability density as a function independent of the orientation of the measuring devices. Then, we use the dynamical evolution of the probability distribution to show that the spin-correlation integral cannot be expressed in terms of initial Cauchy data restricted to the particles. A measurement independence loophole ensues, which prevents the usage of the non-contextual correlation integrals required to demonstrate the CHSH-Bell inequality. We propose that correlated fields are the missing hidden variable triggering the coupled nonlinear oscillations of the particles, which bring about the synchronicities observed in the Einstein–Podolsky–Rosen–Bohm (EPRB) experiment. Full article

Chromatic quantum contextuality is a criterion of quantum nonclassicality based on (hyper)graph coloring constraints. If a quantum hypergraph requires more colors than the number of outcomes per maximal observable (context), it lacks a classical realization with n-uniform outcomes per context. Consequently, it cannot represent a “completable” noncontextual set of coexisting n-ary outcomes per maximal observable. This result serves as a chromatic analogue of the Kochen-Specker theorem. We present an explicit example of a four-colorable quantum logic in dimension three. Furthermore, chromatic contextuality suggests a novel restriction on classical truth values, thereby excluding two-valued measures that cannot be extended to n-ary colorings. Using this framework, we establish new bounds for the house, pentagon, and pentagram hypergraphs, refining previous constraints. Full article

This paper is devoted to an experimental investigation of cognitive contextuality inspired by quantum contextuality research. This contextuality is related to, but not identical to context-sensitivity which is well-studied in cognitive psychology and decision making. This paper is a part of quantum-like modeling, i.e., exploring the methodology of quantum theory outside of physics. We examined the bistable perception of cup-like objects, which strongly depends on experimental contexts. Our experimental data confirmed the existence of cognitive hysteresis, the important role of memory, and the non-commutative structure of cognitive observables. In physics, quantum contextuality is assessed using Bell-CHSH inequalities, and their violation is incorrectly believed to imply the nonlocality of Nature. The violation of Bell-type inequalities in cognitive and social science strongly indicates that the metaphysical implications of these inequalities are quite limited. In our experiments, modified Leggett–Garg inequalities were also significantly violated, but this only means that experimental data from experiments performed in different contexts cannot be modeled by a unique set of noncontextual, jointly distributed random variables. In our experiments, we know the empirical probability distributions measured in different contexts; thus, we can obtain much more detailed and reliable information about contextuality in human cognition by performing nonparametric compatibility tests. Full article

Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement of the independent reality of the system. The most simple case is observed in a three-dimensional Hilbert space, with five different measurement contexts related to each other by shared measurement outcomes. The quantum formalism defines the relations between these contexts in terms of well-defined relations between operators, and these relations can be used to reconstruct an unknown quantum state from a finite set of measurement results. Here, I introduce a reconstruction method based on the relations between the five measurement contexts that can violate the bounds of non-contextual statistics. A complete description of an arbitrary quantum state requires only five of the eight elements of a Kirkwood–Dirac quasiprobability, but only an overcomplete set of eleven elements provides an unbiased description of all five contexts. A set of five fundamental relations between the eleven elements reveals a deterministic structure that links the five contexts. As illustrated by a number of examples, these relations provide a consistent description of contextual realities for the measurement outcomes of all five contexts. Full article

Assessment methodologies such as BREEAM and LEED allocate points based on prescribed interventions that promote design features or strategies considered to be more sustainable than others. A focus on accumulating numerical scores, however, often fails to address pertinent contextual issues, particularly within developing countries. This paper examines the use of four assessment systems in Kenya—two international systems, LEED-US and Green Star SA-Kenya; and two locally developed systems, Green Mark Kenya and the Safari Green Building Index. The paper compares the relative weighting of different categories under each system, and assesses their appropriateness to a Kenyan context, with reference to the suitability of active technology versus passive design approaches. The paper examines selected examples of ‘green’ buildings in Nairobi, reflecting on the influence of different methods of assessment on the adopted design approaches. The paper argues that international rating systems, such as LEED, often focus on a Western construct of sustainability featuring a systematic bias towards global rather than local perspectives, with an emphasis on physical environmental factors. In pursuit of objectivity, the measurement of non-contextual parameters untailored to local circumstances (e.g., energy performance) is prioritised at the expense of those contingent on local conditions or climate. Full article

As social media platforms continue their exponential growth, so do the threats targeting their security. Detecting disguised spam messages poses an immense challenge owing to the constant evolution of tactics. This research investigates advanced artificial intelligence techniques to significantly enhance multiplatform spam classification on Twitter and YouTube. The deep neural networks we use are state-of-the-art. They are recurrent neural network architectures with long- and short-term memory cells that are powered by both static and contextualized word embeddings. Extensive comparative experiments precede rigorous hyperparameter tuning on the datasets. Results reveal a profound impact of tailored, platform-specific AI techniques in combating sophisticated and perpetually evolving threats. The key innovation lies in tailoring deep learning (DL) architectures to leverage both intrinsic platform contexts and extrinsic contextual embeddings for strengthened generalization. The results include consistent accuracy improvements of more than 10–15% in multisource datasets, unlocking actionable guidelines on optimal components of neural models, and embedding strategies for cross-platform defense systems. Contextualized embeddings like BERT and ELMo consistently outperform their noncontextualized counterparts. The standalone ELMo model with logistic regression emerges as the top performer, attaining exceptional accuracy scores of 90% on Twitter and 94% on YouTube data. This signifies the immense potential of contextualized language representations in capturing subtle semantic signals vital for identifying disguised spam. As emerging adversarial attacks exploit human vulnerabilities, advancing defense strategies through enhanced neural language understanding is imperative. We recommend that social media companies and academic researchers build on contextualized language models to strengthen social media security. This research approach demonstrates the immense potential of personalized, platform-specific DL techniques to combat the continuously evolving threats that threaten social media security. Full article

Counterfactual definiteness (CFD) means that if some property is measured in some context, then the outcome of the measurement would have been the same had this property been measured in a different context. A context includes all other measurements made together with the one in question, and the spatiotemporal relations among them. The proviso for CFD is non-disturbance: any physical influence of the contexts on the property being measured is excluded by the laws of nature, so that no one measuring this property has a way of ascertaining its context. It is usually claimed that in quantum mechanics CFD does not hold, because if one assigns the same value to a property in all contexts it is measured in, one runs into a logical contradiction, or at least contravenes quantum theory and experimental evidence. We show that this claim is not substantiated if one takes into account that only one of the possible contexts can be a factual context, all other contexts being counterfactual. With this in mind, any system of random variables can be viewed as satisfying CFD. The concept of CFD is closely related to but distinct from that of noncontextuality, and it is the latter property that may or may not hold for a system, in particular being contravened by some quantum systems. Full article

Bell nonlocality and Kochen–Specker contextuality are among the main topics in the foundations of quantum theory. Both of them are related to stronger-than-classical correlations, with the former usually referring to spatially separated systems, while the latter considers a single system. In recent works, a unified framework for these phenomena was presented. This article reviews, expands, and obtains new results regarding this framework. Contextual and disturbing features inside the local models are explored, which allows for the definition of different local sets with a non-trivial relation among them. The relations between the set of quantum correlations and these local sets are also considered, and post-quantum local behaviours are found. Moreover, examples of correlations that are both local and non-contextual but such that these two classical features cannot be expressed by the same hidden variable model are shown. Extensions of the Fine–Abramsky–Brandenburger theorem are also discussed. Full article

Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize nonsignaling distributions on contextuality scenarios. This paper studies simplicial distributions on two-dimensional measurement spaces by introducing new topological methods. Two key ingredients are a geometric interpretation of Fourier–Motzkin elimination and a technique based on the collapsing of measurement spaces. Using the first one, we provide a new proof of Fine’s theorem characterizing noncontextual distributions in N-cycle scenarios. Our approach goes beyond these scenarios and can describe noncontextual distributions in scenarios obtained by gluing cycle scenarios of various sizes. The second technique is used for detecting contextual vertices and deriving new Bell inequalities. Combined with these methods, we explore a monoid structure on simplicial distributions. Full article

Contextuality was originally defined only for consistently connected systems of random variables (those without disturbance/signaling). Contextuality-by-Default theory (CbD) offers an extension of the notion of contextuality to inconsistently connected systems (those with disturbance) by defining it in terms of the systems’ couplings subject to certain constraints. Such extensions are sometimes met with skepticism. We pose the question of whether it is possible to develop a set of substantive requirements (i.e., those addressing a notion itself rather than its presentation form) such that (1) for any consistently connected system, these requirements are satisfied, but (2) they are violated for some inconsistently connected systems. We show that no such set of requirements is possible, not only for CbD but for all possible CbD-like extensions of contextuality. This follows from the fact that any extended contextuality theory $\mathsf{T}$ is contextually equivalent to a theory ${\mathsf{T}}^{\prime }$ in which all systems are consistently connected. The contextual equivalence means the following: there is a bijective correspondence between the systems in $\mathsf{T}$ and ${\mathsf{T}}^{\prime }$ such that the corresponding systems in $\mathsf{T}$ and ${\mathsf{T}}^{\prime }$ are, in a well-defined sense, mere reformulations of each other, and they are contextual or noncontextual together. Full article

We describe an explicitly non-contextual statistical model of hidden variables for the qutrit, which fully reproduces the predictions of quantum mechanics, and thus, bypasses the constraints imposed by the Kochen–Specker theorem and its subsequent reformulations. We notice that these renowned theorems crucially rely on the implicitly assumed existence of an absolute frame of reference with respect to which physically indistinguishable tests related by spurious gauge transformations can supposedly be assigned well-defined distinct identities. We observe that the existence of such an absolute frame of reference is not required by fundamental physical principles, and hence, assuming it is an unnecessarily restrictive demand. Full article

A noncontextual system of random variables may become contextual if one adds to it a set of new variables, even if each of them is obtained by the same context-wise function of the old variables. This fact follows from the definition of contextuality, and its demonstration is trivial for inconsistently connected systems (i.e., systems with disturbance). However, it also holds for consistently connected (and even strongly consistently connected) systems, provided one acknowledges that if a given property was not measured in a given context, this information can be used in defining functions among the random variables. Moreover, every inconsistently connected system can be presented as a (strongly) consistently connected system with essentially the same contextuality characteristics. Full article

Detecting vulnerabilities in programs is an important yet challenging problem in cybersecurity. The recent advancement in techniques of natural language understanding enables the data-driven research on automated code analysis to embrace Pre-trained Contextualized Models (PCMs). These models are pre-trained on the large corpus and can be fine-tuned for various downstream tasks, but their feasibility and effectiveness for software vulnerability detection have not been systematically studied. In this paper, we explore six prevalent PCMs and compare them with three mainstream Non-Contextualized Models (NCMs) in terms of generating effective function-level representations for vulnerability detection. We found that, although the detection performance of PCMs outperformed that of the NCMs, training and fine-tuning PCMs were computationally expensive. The budgets for deployment and inference are also considerable in practice, which may prevent the wide adoption of PCMs in the field of interest. However, we discover that, when the PCMs were compressed using the technique of knowledge distillation, they achieved similar detection performance but with significantly improved efficiency compared with their uncompressed counterparts when using 40,000 synthetic C functions for fine-tuning and approximately 79,200 real-world C functions for training. Among the distilled PCMs, the distilled CodeBERT achieved the most cost-effective performance. Therefore, we proposed a framework encapsulating the Distilled CodeBERT for an end-to-end Vulnerable function Detection (named DistilVD). To examine the performance of the proposed framework in real-world scenarios, DistilVD was tested on four open-source real-world projects with a small amount of training data. Results showed that DistilVD outperformed the five baseline approaches. Further evaluations on multi-class vulnerability detection also confirmed the effectiveness of DistilVD for detecting various vulnerability types. Full article