  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.
