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arXiv · 2003.08224

A Diagrammatic Approach to Information Transmission in Generalised Switches

Matt Wilson·Giulio Chiribella
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Abstract

The quantum switch is a higher-order operation that takes as an input two quantum processes and combines them in a coherent superposition of two alternative orders. Here we provide an approach to the quantum switch based on the methods of categorical quantum mechanics. Specifically, we represent the quantum switch as a sum of diagrams in the category of finite dimensional Hilbert spaces, or, equivalently, as a sum of diagrams built from Selinger's CPM construction. The sum-of-diagrams picture provides intuition for the activation of classical capacity of completely depolarising channels (CDPCs) and allows for generalisation to N-channel switches. We demonstrate the use of these partially diagrammatic methods by deriving a permutation condition for computing the output of any N-channel switch of CDPCs, we then use that condition to prove that amongst all possible terms, the interference terms associated to cyclic permutations of the N channels are the information-transmitting terms with maximum normalisation

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Matt Wilson, Giulio Chiribella. 2021-09-06. A Diagrammatic Approach to Information Transmission in Generalised Switches. https://doi.org/10.4204/eptcs.340.17

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