Reply to comments arXiv:2512.07881 and arXiv:2601.06104 on quantum structure in human and AI-generated language

Massimiliano Sassoli de Bianchi; Roberto Leporini

cs.CLSep 22, 2026

Reply to comments arXiv:2512.07881 and arXiv:2601.06104 on quantum structure in human and AI-generated language

Authors: Massimiliano Sassoli de Bianchi, Roberto Leporini

Organizations: Center Leo Apostel for Interdisciplinary Studies, Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium · Department of Economics, University of Bergamo, via dei Caniana 2, Bergamo, 24127, Italy

Abstract

We reply to the comments by M. Sienicki and K. Sienicki (arXiv:2512.07881) and by K. Sienicki (arXiv:2601.06104) on our work on quantum-mechanical statistics in human language (arXiv:2407.14924) and on quantum structure in AI-generated language (arXiv:2511.21731). We thank the authors for their careful reading and address what we consider to be the main points of criticism: the exploratory nature of the protocol used in the experiments with large language models; the role of marginal-law violations, and of the Contextuality-by-Default criterion, in the identification of entanglement; the limited diagnostic value of a Bose-Einstein fit taken in isolation; the meaning of assigning the lowest energy levels to the most frequent words; and the relation between the vector spaces used by LLMs and quantum state spaces. We also correct a typographical error in Table 3 of arXiv:2511.21731, which does not affect the reported CHSH value.

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Separating quantum circuits from classical LLMs

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Quantum Circuits Large Language Model Quantization Strong Large Language Model Diffusion Language Models Transformer Encoder Circuits+2

Open paper AskPDF arXiv

Modern large language models - transformers and diffusion language models - are built around two canonical algorithmic tasks: prediction and generation. We prove unconditional separations between low-depth quantum computation and the corresponding bounded-resource classical language-model architectures in both regimes. Concretely, we exhibit the following: 1. Distributional separation. We give a distribution that is sampleable by

\textsf{QNC}^0

circuits (i.e., a family of constant-depth quantum circuits consisting of bounded fan-in gates) that no constant-round diffusion language model (

\textsf{DLM}

) with shallow scheduling and denoising can sample within constant distance, even when allowed sublinear chain-of-thought and output-token revision/remasking events, the very features modern

\textsf{DLM}

s rely on. 2. Functional separation. We exhibit a function computable in

\land \circ \textsf{QNC}^0[\log\log n]

(i.e., a family of O

(\log\log n)

-depth

\textsf{QNC}^0

circuits, where

n

is the input length, followed by a single classical

\mathsf{AND}

gate) such that any constant-depth decoder-only transformer computing the function must be large: it would have to have width

n^{Ω(1)}

. Together, our work initiates the study of quantum advantage in the era of large language models.

Abstract

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