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Quantum Physics

arXiv:2102.08711v4 (quant-ph)
[Submitted on 17 Feb 2021 (v1), last revised 13 Sep 2021 (this version, v4)]

Title:Bennett and Stinespring, Together at Last

Authors:Chris Heunen (University of Edinburgh), Robin Kaarsgaard (University of Edinburgh)
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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.
Comments: In Proceedings QPL 2021, arXiv:2109.04886
Subjects: Quantum Physics (quant-ph); Logic in Computer Science (cs.LO); Category Theory (math.CT)
Cite as: arXiv:2102.08711 [quant-ph]
  (or arXiv:2102.08711v4 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.2102.08711
Journal reference: EPTCS 343, 2021, pp. 102-118
Related DOI: https://doi.org/10.4204/EPTCS.343.5

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Wed, 17 Feb 2021 11:50:12 UTC (253 KB)
[v2] Tue, 2 Mar 2021 18:23:39 UTC (255 KB)
[v3] Wed, 19 May 2021 10:44:09 UTC (247 KB)
[v4] Mon, 13 Sep 2021 00:51:44 UTC (28 KB)
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