Locally Tomographic Shadows (Extended Abstract)

• URL: http://arxiv.org/abs/2308.16494v1
• Date: Thu, 31 Aug 2023 06:57:20 GMT
• Title: Locally Tomographic Shadows (Extended Abstract)
• Authors: Howard Barnum, Matthew A. Graydon (Institute for Quantum Computing, University of Waterloo), Alex Wilce (Susquehanna University)
• Abstract summary: LT$(mathcalC,mathbfV)$ describes phenomena observable by local agents controlling systems. Some globally distinct states become locally indistinguishable in LT$(mathcalC,mathbfV)$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Given a monoidal probabilistic theory -- a symmetric monoidal category $\mathcal{C}$ of systems and processes, together with a functor $\mathbf{V}$ assigning concrete probabilistic models to objects of $\mathcal{C}$ -- we construct a locally tomographic probabilistic theory LT$(\mathcal{C},\mathbf{V})$ -- the locally tomographic shadow of $(\mathcal{C},\mathbf{V})$ -- describing phenomena observable by local agents controlling systems in $\mathcal{C}$, and able to pool information about joint measurements made on those systems. Some globally distinct states become locally indistinguishable in LT$(\mathcal{C},\mathbf{V})$, and we restrict the set of processes to those that respect this indistinguishability. This construction is investigated in some detail for real quantum theory.

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