The qufinite ZXW calculus is complete for the category FHilb of finite-dimensional Hilbert spaces, as any diagram rewrites to a unique normal form.
Categorical quantum mechanics
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abstract
This invited chapter in the Handbook of Quantum Logic and Quantum Structures consists of two parts: 1. A substantially updated version of quant-ph/0402130 by the same authors, which initiated the area of categorical quantum mechanics, but had not yet been published in full length; 2. An overview of the progress which has been made since then in this area.
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Completeness of qufinite ZXW calculus, a graphical language for finite-dimensional quantum theory
The qufinite ZXW calculus is complete for the category FHilb of finite-dimensional Hilbert spaces, as any diagram rewrites to a unique normal form.