Identifying Quantum Structure in AI Language: Evidence for Evolutionary Convergence of Human and Artificial Cognition

📝 Abstract

We present the results of cognitive tests on conceptual combinations, performed using specific Large Language Models (LLMs) as test subjects. In the first test, performed with ChatGPT and Gemini, we show that Bell’s inequalities are significantly violated, which indicates the presence of ‘quantum entanglement’ in the tested concepts. In the second test, also performed using ChatGPT and Gemini, we instead identify the presence of ‘Bose-Einstein statistics’, rather than the intuitively expected ‘Maxwell-Boltzmann statistics’, in the distribution of the words contained in large-size texts. Interestingly, these findings mirror the results previously obtained in both cognitive tests with human participants and information retrieval tests on large corpora. Taken together, they point to the ‘systematic emergence of quantum structures in conceptual-linguistic domains’, regardless of whether the cognitive agent is human or artificial. Although LLMs are classified as neural networks for historical reasons, we believe that a more essential form of knowledge organization takes place in the distributive semantic structure of vector spaces built on top of the neural network. It is this meaning-bearing structure that lends itself to a phenomenon of evolutionary convergence between human cognition and language, slowly established through biological evolution, and LLM cognition and language, emerging much more rapidly as a result of self-learning and training. We analyze various aspects and examples that contain evidence supporting the above hypothesis. We also advance a unifying framework that explains the pervasive quantum organization of meaning that we identify.

💡 Analysis

We present the results of cognitive tests on conceptual combinations, performed using specific Large Language Models (LLMs) as test subjects. In the first test, performed with ChatGPT and Gemini, we show that Bell’s inequalities are significantly violated, which indicates the presence of ‘quantum entanglement’ in the tested concepts. In the second test, also performed using ChatGPT and Gemini, we instead identify the presence of ‘Bose-Einstein statistics’, rather than the intuitively expected ‘Maxwell-Boltzmann statistics’, in the distribution of the words contained in large-size texts. Interestingly, these findings mirror the results previously obtained in both cognitive tests with human participants and information retrieval tests on large corpora. Taken together, they point to the ‘systematic emergence of quantum structures in conceptual-linguistic domains’, regardless of whether the cognitive agent is human or artificial. Although LLMs are classified as neural networks for historical reasons, we believe that a more essential form of knowledge organization takes place in the distributive semantic structure of vector spaces built on top of the neural network. It is this meaning-bearing structure that lends itself to a phenomenon of evolutionary convergence between human cognition and language, slowly established through biological evolution, and LLM cognition and language, emerging much more rapidly as a result of self-learning and training. We analyze various aspects and examples that contain evidence supporting the above hypothesis. We also advance a unifying framework that explains the pervasive quantum organization of meaning that we identify.

📄 Content

Identifying Quantum Structure in AI Language: Evidence for Evolutionary Convergence of Human and Artificial Cognition Diederik Aerts∗, Jonito Aerts Argu¨elles∗, Lester Beltran∗, Suzette Geriente∗, Massimiliano Sassoli de Bianchi∗, Roberto Leporini† and Sandro Sozzo‡ Abstract We present the results of cognitive tests on conceptual combinations, performed using specific Large Language Models (LLMs) as test subjects. In the first test, performed with ChatGPT and Gemini, we show that Bell’s inequalities are significantly violated, which indicates the presence of ‘quantum entanglement’ in the tested concepts. In the second test, also performed using ChatGPT and Gemini, we identify the presence of ‘Bose- Einstein statistics’, rather than the intuitively expected ‘Maxwell-Boltzmann statistics’, in the distribution of the words contained in large-size texts. Interestingly, these findings mirror the results previously obtained in both cognitive tests with human participants and information retrieval tests on large corpora. Taken together, they point to the ‘systematic emergence of quantum structures in conceptual-linguistic domains’, regardless of whether the cognitive agent is human or artificial. Although LLMs are classified as neural networks for historical reasons, we believe that a more essential form of knowledge organization takes place in the distributive semantic structure of vector spaces built on top of the neural network. It is this meaning-bearing structure that lends itself to a phenomenon of evolutionary convergence between human cognition and language, slowly established through biological evolution, and LLM cognition and language, emerging much more rapidly as a result of self-learning and training. We analyze various aspects and examples that contain evidence supporting the above hypothesis. We also advance a unifying framework that explains the pervasive quantum organization of meaning that we identify. Keywords: Human cognition, Artificial Intelligence, Large Language Models, Quantum structures, Entanglement, Bose-Einstein statistics ∗Center Leo Apostel for Interdisciplinary Studies, Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium; email addresses: diraerts@vub.be, jonitoarguelles@gmail.com, lestercc21@yahoo.com, sge- riente83@yahoo.com, autoricerca@gmail.com †Department of Economics, University of Bergamo, via dei Caniana 2, Bergamo, 24127, Italy; email address: roberto.leporini@unibg.it ‡Department of Humanities and Cultural Heritage (DIUM) and Centre CQSCS, University of Udine, Vicolo Florio 2/b, 33100 Udine, Italy; email address: sandro.sozzo@uniud.it 1 arXiv:2511.21731v1 [cs.CL] 21 Nov 2025 1 Introduction In this study, we performed and analyzed experiments testing Bell inequalities and quantum statistics in the cognitive domain, using large language models (LLMs) as test subjects. As we shall see, LLMs violate Bell’s inequalities and explicitly exhibit quantum statistics in the texts they produce. It is within the research domain known as quantum cognition (Aerts & Aerts, 1995; Gabora & Aerts, 2002; Bruza & Cole, 2005; Aerts & Gabora, 2005a,b; Busemeyer et al., 2006; Aerts, 2009a,b; Bruza & Gabora, 2009; Aerts & Sozzo, 2011; Aerts et al., 2012; Busemeyer & Bruza, 2012; Haven & Khrennikov, 2013; Dalla Chiara et al., 2015; Pothos et al., 2015; Blutner & beim Graben, 2016; Moreira & Wichert, 2016; Gabora & Kitto, 2017; Surov et al., 2019; Aerts & Beltran, 2020, 2022a), where structures, such as the quantum probability model, but also the complex Hilbert space of quantum mechanics, are used to describe phenomena of human language and of human cognition, that we study this situation of LLMs being test subjects. This will allow us to highlight surprising aspects of the cognitive capabilities of LLMs that remain underexposed in current studies. In 1964, John Bell proved that, if one introduces local realism as a hypothesis for a physical theory, then one can derive an inequality for the expectation values of suitable physical observables (‘Bell’s inequality’) which is violated in quantum mechanics Bell (1964). This violation is due to a feature of quantum mechanics which is called ‘entanglement’. But the violation of Bell’s inequalities also proves the impossibility to cast the observed quantum probabilities into a classical Kolmogorovian probability space Kolmogorov (1932); Aerts (1986); Pitowski (1989). One generally concludes that, because of entanglement, one cannot consider the component parts of a composite quantum system, or ‘entity’, separately, but the entity must be described as an undivided whole. The way in which Bell’s inequalities are violated and how this is proven by the tested LLMs touches on all three of the above cases (entanglement, non-Kolmogorovianity and wholeness) but is also specific to how quantum structures emerge in cognition and the information exchange that accompanies it, as we will clarify in the next section. When it comes to large collectio

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