Priyaa Srinivasan

Title: Quantum Channels for Mixed Unitary Categories
Abstract: Categorically, quantum processes are modelled as completely positive maps in dagger compact closed categories [1,2,3]. The limitation however is that the quantum processes modelled are for finite-dimensional systems. A natural setting for quantum processes between infinite dimensional systems is a *-autonomous category or more generally a linearly distributive category. The goal of my talk is to introduce dagger linearly distributive categories and mixed unitary categories in which one can discuss about quantum processes possibly in infinite dimensions. CP-infinity construction [4] on dagger symmetric monoidal categories generalizes CPM construction [3] to arbitrary dimensions. I will show a generalization of CP-infinity construction to mixed unitary categories.
References:
[1] Bob Coecke, Chris Heunen, and Aleks Kissinger. Categories of quantum and classical channels. Quantum Information Processing, 15(12):5179–5209, December 2016.
[2] Bob Coecke and Aleks Kissinger. Picturing Quantum Processes. Cambridge University Press, Cambridge, England, 2017.
[3] Peter Selinger. Dagger compact closed categories and completely positive maps. Electronic Notes in Theoretical Computer Science, 170:139–163, 2007.
[4] Coecke, Bob, and Chris Heunen. Pictures of complete positivity in arbitrary dimension. Information and Computation 250 (2016): 50-58.