PIRSA:23040162

Causal decompositions of unitary maps

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

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

          @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

Talk number
PIRSA:23040162
Collection
Talk Type
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