arXiv subjects

Victor H. Cervantes

Publications and source records attributed to Victor H. Cervantes.

8 recordsLinked to original sources

arXiv2026

Degrees, Levels, and Profiles of Contextuality

We introduce a new notion, that of a contextuality profile of a system of random variables. Rather than characterizing a system's contextuality by a single number, its overall degree of contextuality, we show how it can be characterized by a curve relating degree of contextuality to level at which the system is considered. A system is represented at level n if one only considers the joint distributions with no more than n variables, ignoring higher-order joint distributions. We show that the level-wise contextuality analysis can be used in conjunction with any well-constructed measure of contextuality. We present a method of concatenated systems to explore contextuality profiles systematically, and we apply it to the contextuality profiles for three major measures of contextuality proposed in the literature.

quant-ph↗

arXiv2023

Hypercyclic systems of measurements and patterns of contextuality

We consider four measures of contextuality, chosen for being based on the fundamental properties of the notion of contextuality, and for being applicable to arbitrary systems of measurements, both without and with disturbance. We have previously shown that no two of them are functions of each other: as systems of measurements change, either of them can change, while the other remains constant. This means that they measure different aspects of contextuality, and we proposed that rather than picking just one measure of contextuality in one specific sense, one could use all of them to characterize a contextual system by its pattern of contextuality. To study patterns of contextuality, however, one needs a systematic way of varying systems of measurements, which requires their convenient parametrization. We have convenient parametrization within the class of cyclic systems that have played a dominant role in the foundations of quantum mechanics. However, they cannot be used to study patterns of contextuality, because within this class the four measures of contextuality have been shown to be proportional to each other. In this concept paper, we introduce hypercyclic systems of measurements. They generalize cyclic systems while preserving convenient parametrization. We show that within this class of systems, the same as for systems at large, no two of the measures of contextuality are functions of each other. This means that hypercyclic systems can be used to study patterns of contextuality.

quant-ph↗

arXiv2021

On the Quantum-like Contextuality of Ambiguous Phrases

Language is contextual as meanings of words are dependent on their contexts. Contextuality is, concomitantly, a well-defined concept in quantum mechanics where it is considered a major resource for quantum computations. We investigate whether natural language exhibits any of the quantum mechanics' contextual features. We show that meaning combinations in ambiguous phrases can be modelled in the sheaf-theoretic framework for quantum contextuality, where they can become possibilistically contextual. Using the framework of Contextuality-by-Default (CbD), we explore the probabilistic variants of these and show that CbD-contextuality is also possible.

cs.CL↗

arXiv2019

True Contextuality in a Psychophysical Experiment

Recent crowdsourcing experiments have shown that true contextuality of the kind found in quantum mechanics can also be present in human behavior. In these experiments simple human choices were aggregated over large numbers of respondents, with each respondent dealing with a single context (set of questions asked). In this paper we present experimental evidence of contextuality in individual human behavior, in a psychophysical experiment with repeated presentations of visual stimuli in randomly varying contexts (arrangements of stimuli). The analysis is based on the Contextuality-by-Default (CbD) theory whose relevant aspects are reviewed in the paper. CbD allows one to detect contextuality in the presence of direct influences, i.e., when responses to the same stimuli have different distributions in different contexts. The experiment presented is also the first one in which contextuality is demonstrated for responses that are not dichotomous, with five options to choose among. CbD requires that random variables representing such responses be dichotomized before they are subjected to contextuality analysis. A theorem says that a system consisting of all possible dichotomizations of responses has to be contextual if these responses violate a certain condition, called nominal dominance. In our experiment nominal dominance was violated in all data sets, with very high statistical reliability established by bootstrapping.

q-bio.NC↗

arXiv2018

Snow Queen is Evil and Beautiful: Experimental Evidence for Probabilistic Contextuality in Human Choices

We present unambiguous experimental evidence for (quantum-like) probabilistic contextuality in psychology. All previous attempts to find contextuality in a psychological experiment were unsuccessful because of the gross violations of marginal selectivity in behavioral data, making the traditional mathematical tests developed in quantum mechanics inapplicable. In our crowdsourcing experiment respondents were making two simple choices: of one of two characters in a story (The Snow Queen by Hans Christian Andersen), and of one of two characteristics, such as Kind and Evil, so that the character and the characteristic chosen matched the story line. The formal structure of the experiment imitated that of the Einstein-Podolsky-Rosen paradigm in the Bohm-Bell version. Marginal selectivity was violated, indicating that the two choices were directly influencing each other, but the application of a mathematical test developed in the Contextuality-by-Default theory, extending the traditional quantum-mechanical test, indicated a strong presence of contextuality proper, not reducible to direct influences.

q-bio.NC↗

arXiv2016

Exploration of Contextuality in a Psychophysical Double-Detection Experiment

The Contextuality-by-Default (CbD) theory allows one to separate contextuality from context-dependent errors and violations of selective influences (aka "no-signaling" or "no-disturbance" principles). This makes the theory especially applicable to behavioral systems, where violations of selective influences are ubiquitous. For cyclic systems with binary random variables, CbD provides necessary and sufficient conditions for noncontextuality, and these conditions are known to be breached in certain quantum systems. We apply the theory of cyclic systems to a psychophysical double-detection experiment, in which observers were asked to determine presence or absence of a signal property in each of two simultaneously presented stimuli. The results, as in all other behavioral and social systems previous analyzed, indicate lack of contextuality. The role of context in double-detection is confined to lack of selectiveness: the distribution of responses to one of the stimuli is influenced by the state of the other stimulus.

q-bio.NC↗

arXiv2016

On Contextuality in Behavioral Data

Dzhafarov, Zhang, and Kujala (Phil. Trans. Roy. Soc. A 374, 20150099) reviewed several behavioral data sets imitating the formal design of the quantum-mechanical contextuality experiments. The conclusion was that none of these data sets exhibited contextuality if understood in the generalized sense proposed in Dzhafarov, Kujala, and Larsson (Found. Phys. 7, 762-782, 2015), while the traditional definition of contextuality does not apply to these data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signaling condition, no-disturbance principle, etc.). In this paper we clarify the relationship between (in)consistent connectedness and (non)contextuality, as well as between the traditional and extended definitions of (non)contextuality, using as an example the Clauser-Horn-Shimony-Holt (CHSH) inequalities originally designed for detecting contextuality in entangled particles.

q-bio.NC↗

arXiv2015

Contextuality-by-Default: A Brief Overview of Ideas, Concepts, and Terminology

This paper is a brief overview of the concepts involved in measuring the degree of contextuality and detecting contextuality in systems of binary measurements of a finite number of objects. We discuss and clarify the main concepts and terminology of the theory called "contextuality-by-default," and then discuss a possible generalization of the theory from binary to arbitrary measurements.

quant-ph↗