# Bennett and Stinespring, Together at Last

arXiv: https://arxiv.org/abs/2102.08711 · HTML: https://mlsanity.com/paper/2102.08711/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2021.

## Built on by (most cited first, 1 of 1)

- [Jeopardy: An Invertible Functional Programming Language](https://mlsanity.com/paper/2209.02422/) (2022)

## Abstract (arXiv)

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.