A diagrammatic calculus for categorical quantum protocols
- URL: http://arxiv.org/abs/2206.03294v3
- Date: Sat, 18 Nov 2023 09:42:25 GMT
- Title: A diagrammatic calculus for categorical quantum protocols
- Authors: Dusan Dordevic, Zoran Petric, Mladen Zekic
- Abstract summary: We show an explicit realisation of a category with enough structure to check the validity of a certain class of quantum protocols.
In particular, we show the validity of quantum teleportation, entanglement swapping and superdense coding protocol.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: As shown by Abramsky and Coecke, quantum mechanics can be studied in terms of
dagger compact closed categories with biproducts. Within this structure, many
well-known quantum protocols can be described and their validity can be shown
by establishing the commutativity of certain diagrams in that category. In this
paper, we propose an explicit realisation of a category with enough structure
to check the validity of a certain class of quantum protocols. In order to do
this, we construct a category based on 1-dimensional cobordisms with attached
elements of a certain group freely generated by a finite set. We use this
category as a graphical language, and we show that it is dagger compact closed
with biproducts. Then, relying on the coherence result for compact closed
categories, proved by Kelly and Laplaza, we show the coherence result, which
enables us to check the validity of quantum protocols just by drawing diagrams.
In particular, we show the validity of quantum teleportation, entanglement
swapping (as formulated in the work of Abramsky and Coecke) and superdense
coding protocol.
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