2020/03/31 by Matt Wilson, Giulio Chiribella
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.4204/eptcs.340.17
published as EPTCS 340, 2021, pp. 333-348 · In Proceedings QPL 2020, arXiv:2109.01534
arxiv created 2021/09/06 · arxiv updated 2021/09/07
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