# Open System Categorical Quantum Semantics in Natural Language Processing

arXiv: https://arxiv.org/abs/1502.00831 · HTML: https://mlsanity.com/paper/1502.00831/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2015.

## Built on by (most cited first, 17 of 17)

- [QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer](https://mlsanity.com/paper/2102.12846/) (2021)
- [A CCG-Based Version of the DisCoCat Framework](https://mlsanity.com/paper/2105.07720/) (2021)
- [Compositionality as we see it, everywhere around us](https://mlsanity.com/paper/2110.05327/) (2021)
- [Conversational Negation using Worldly Context in Compositional Distributional Semantics](https://mlsanity.com/paper/2105.05748/) (2021)
- [Composing Conversational Negation](https://mlsanity.com/paper/2107.06820/) (2021)
- [Distilling Text into Circuits](https://mlsanity.com/paper/2301.10595/) (2023)
- [On the Quantum-like Contextuality of Ambiguous Phrases](https://mlsanity.com/paper/2107.14589/) (2021)
- [Near-Term Advances in Quantum Natural Language Processing](https://mlsanity.com/paper/2206.02171/) (2022)
- [On Meta-Prompting](https://mlsanity.com/paper/2312.06562/) (2023)
- [How to make qubits speak](https://mlsanity.com/paper/2107.06776/) (2021)
- [Grover's Algorithm for Question Answering](https://mlsanity.com/paper/2106.05299/) (2021)
- [Functorial Language Models](https://mlsanity.com/paper/2103.14411/) (2021)
- [The Causal Structure of Semantic Ambiguities](https://mlsanity.com/paper/2206.06807/) (2022)
- [Traitement quantique des langues : 'etat de l'art](https://mlsanity.com/paper/2406.15370/) (2024)
- [Density Matrices for Metaphor Understanding](https://mlsanity.com/paper/2408.11846/) (2024)
- [Quantum Methods for Managing Ambiguity in Natural Language Processing](https://mlsanity.com/paper/2504.00040/) (2025)
- [Efficient Generation of Parameterised Quantum Circuits from Large Texts](https://mlsanity.com/paper/2505.13208/) (2025)

## Abstract (arXiv)

Originally inspired by categorical quantum mechanics (Abramsky and Coecke, LiCS'04), the categorical compositional distributional model of natural language meaning of Coecke, Sadrzadeh and Clark provides a conceptually motivated procedure to compute the meaning of a sentence, given its grammatical structure within a Lambek pregroup and a vectorial representation of the meaning of its parts. The predictions of this first model have outperformed that of other models in mainstream empirical language processing tasks on large scale data. Moreover, just like CQM allows for varying the model in which we interpret quantum axioms, one can also vary the model in which we interpret word meaning. In this paper we show that further developments in categorical quantum mechanics are relevant to natural language processing too. Firstly, Selinger's CPM-construction allows for explicitly taking into account lexical ambiguity and distinguishing between the two inherently different notions of homonymy and polysemy. In terms of the model in which we interpret word meaning, this means a passage from the vector space model to density matrices. Despite this change of model, standard empirical methods for comparing meanings can be easily adopted, which we demonstrate by a small-scale experiment on real-world data. This experiment moreover provides preliminary evidence of the validity of our proposed new model for word meaning. Secondly, commutative classical structures as well as their non-commutative counterparts that arise in the image of the CPM-construction allow for encoding relative pronouns, verbs and adjectives, and finally, iteration of the CPM-construction, something that has no counterpart in the quantum realm, enables one to accommodate both entailment and ambiguity.