A Diagrammatic Approach to Information Transmission in Generalised Switches

• URL: http://arxiv.org/abs/2003.08224v3
• Date: Mon, 6 Sep 2021 01:03:56 GMT
• Title: A Diagrammatic Approach to Information Transmission in Generalised Switches
• Authors: Matt Wilson, Giulio Chiribella
• Abstract summary: We provide an approach to the quantum switch based on the methods of categorical quantum mechanics. We represent the quantum switch as a sum of diagrams in the category of finite dimensional Hilbert spaces.
• Score: 0.7614628596146599
• License: http://creativecommons.org/licenses/by/4.0/
• 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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