Locally Tomographic Shadows (Extended Abstract)
Howard Barnum, Matthew A. Graydon (Institute for Quantum Computing,, University of Waterloo), Alex Wilce (Susquehanna University)

TL;DR
This paper introduces a framework for constructing locally tomographic probabilistic theories from monoidal categories, highlighting how global states can become indistinguishable locally, with detailed analysis in the context of real quantum theory.
Contribution
It develops a method to derive locally tomographic shadows of monoidal probabilistic theories, clarifying local indistinguishability phenomena and process restrictions, especially in real quantum theory.
Findings
Locally tomographic shadows capture local indistinguishability of states.
The construction restricts processes to respect local indistinguishability.
Application to real quantum theory illustrates the framework.
Abstract
Given a monoidal probabilistic theory -- a symmetric monoidal category of systems and processes, together with a functor assigning concrete probabilistic models to objects of -- we construct a locally tomographic probabilistic theory LT -- the locally tomographic shadow of -- describing phenomena observable by local agents controlling systems in , and able to pool information about joint measurements made on those systems. Some globally distinct states become locally indistinguishable in LT, and we restrict the set of processes to those that respect this indistinguishability. This construction is investigated in some detail for real quantum theory.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
