Bennett and Stinespring, Together at Last

• URL: http://arxiv.org/abs/2102.08711v4
• Date: Mon, 13 Sep 2021 00:51:44 GMT
• Title: Bennett and Stinespring, Together at Last
• Authors: Chris Heunen (University of Edinburgh), Robin Kaarsgaard (University of Edinburgh)
• Abstract summary: We present a universal construction that relates reversible dynamics on open systems to arbitrary dynamics on closed systems. We show how our construction can be essentially 'undone' by a further universal construction.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a universal construction that relates reversible dynamics on open systems to arbitrary dynamics on closed systems: the restriction affine completion of a monoidal restriction category quotiented by well-pointedness. This categorical completion encompasses both quantum channels, via Stinespring dilation, and classical computing, via Bennett's method. Moreover, in these two cases, we show how our construction can be essentially 'undone' by a further universal construction. This shows how both mixed quantum theory and classical computation rest on entirely reversible foundations.

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