Quantum Coherence Spaces Revisited: A von Neumann (Co)Algebraic Approach
summary
Presents a concrete categorical model of MALL built inside finite-dimensional operator spaces and finite-dimensional von Neumann (co)algebras, using the Haagerup tensor and involutive (co)monoid objects; claims CPTP as positive proofs and CPU as negative proofs and shows operator-space duality yields a strong monoidal equivalence between the Schrödinger and Heisenberg categories. Uses double gluing and orthogonality to build a category Q whose embeddings are fully faithful, recovering exactly CPU/CPTP channels and preserving (co)products.
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chapters (9)
- 0:00Quantum coherence spaces intro
- 1:11Critique of existing approaches
- 3:42Heisenberg vs Schrödinger views
- 5:50Operator spaces foundation
- 7:14Category of finite-dim spaces
- 9:20Von Neumann algebras & duals
- 12:32Linear logic fragments
- 14:40Quantum channels via double gluing
- 16:48Summary of the model
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