# Causal decompositions of unitary maps

### APA

Lorenz, R. (2023). Causal decompositions of unitary maps. Perimeter Institute. https://pirsa.org/23040162

### MLA

Lorenz, Robin. Causal decompositions of unitary maps. Perimeter Institute, Apr. 27, 2023, https://pirsa.org/23040162

### BibTex

@misc{ pirsa_PIRSA:23040162, doi = {10.48660/23040162}, url = {https://pirsa.org/23040162}, author = {Lorenz, Robin}, keywords = {Quantum Foundations}, language = {en}, title = {Causal decompositions of unitary maps}, publisher = {Perimeter Institute}, year = {2023}, month = {apr}, note = {PIRSA:23040162 see, \url{https://pirsa.org}} }

Robin Lorenz Quantinuum

**Collection**

**Talk Type**Scientific Series

**Subject**

## Abstract

Every unitary map with a factorisation of domain and codomain into subsystems has a well-defined causal structure given by the set of influence relations between its input and output subsystems. A causal decomposition of a unitary map U is, roughly, one that makes all there is to know about U in terms of causal structure evident and understandable in compositional terms. We'll argue that this is more than just about drawing more intuitive pictures for the causal structure of U -- it is about really understanding it at all. Now, it has been known for a while that decompositions in terms of ordinary circuit diagrams do not suffice to this end and that at least so called 'extended circuit diagrams', or 'routed circuit diagrams' are necessary, revealing a close connection between causal structure and algebraic structures that involve a particular interplay of direct sum and tensor product. Though whether or not these sorts of routed circuit diagrams suffice has been an open question since. I will give an introduction and overview of this business of causal decompositions of unitary maps, and share what is an on-going thriller.

Zoom link: https://pitp.zoom.us/j/95689128162?pwd=RFNqWlVHMFV0RjRaakszSTBsWkZkUT09