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Categorical Quantum Mechanics II: Classical-Quantum Interaction | | Bob Coecke
; Aleks Kissinger
; | | Date: |
27 May 2016 | | Abstract: | This is the second part of a three-part overview, in which we derive the
category-theoretic backbone of quantum theory from a process ontology, treating
quantum theory as a theory of systems, processes and their interactions. In
this part we focus on classical-quantum interaction.
Classical and quantum systems are treated as distinct types, of which the
respective behavioural properties are specified in terms of processes and their
compositions. In particular, classicality is witnessed by ’spiders’ which fuse
together whenever they connect. We define mixedness and show that pure
processes are extremal in the space of all processes, and we define
entanglement and show that quantum theory indeed exhibits entanglement. We
discuss the classification of tripartite qubit entanglement and show that both
the GHZ-state and the W-state come from spider-like families of processes,
which differ only in how they behave when they are connected by two or more
wires. We define measurements and provide fully-comprehensive descriptions of
several quantum protocols involving classical data flow. Finally, we give a
notion of ’genuine quantumness’, from which special processes called ’phase
spiders’ arise, and get a first glimpse of quantum non-locality. | | Source: | arXiv, 1605.8617 | | Services: | Forum | Review | PDF | Favorites | |
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