Title: Measurement for Mixed Unitary Categories
Abstract:
Mixed Unitary Categories (MUCs) [1] provide a generalization for the finite-dimensional categorical quantum mechanic framework of dagger compact closed categories (dagger KCCs) by introducing dagger structure to Linearly Distributive Categories (LDCs). The goal of this generalization is to develop a framework that will accommodate quantum systems of arbitrary dimensions without forgoing the rich structures of dagger-KCCs. In our previous work, we demonstrated that one can describe quantum processes a.k.a. completely positive maps in the MUC framework. In this talk, I will show how one can describe quantum measurements with this framework. We observe that in the MUC framework, a measurement occurs in two steps – compaction into a unitary core followed by traditional measurement. We also note that, while compacting, structures on the domain type can be transferred to the codomain type. Finally, in alignment with the purpose of MUCs, we note that in the presence of free exponential modalities, every pair of complementary measurements within a unitary core, arises as a compaction of a ‘linear bialgbera’ on exponential modalities.
References:
[1]. Cockett, Robin, Cole Comfort, and Priyaa Srinivasan. “Dagger linear logic for categorical quantum mechanics.” arXiv preprint arXiv:1809.00275 (2018).
