A Process-Theoretic Church of the Larger Hilbert Space

Stefano Gogioso

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arXiv · 1905.13117

A Process-Theoretic Church of the Larger Hilbert Space

Stefano Gogioso

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Abstract

We show how to reconstruct a process theory of local systems starting from a global theory of reversible processes on a single global system, by using the purification principle. In such a process theory, local systems are not given, but rather `emerge' as the global system is decomposed into subsystems. Local systems thus have specific identities and their composition is naturally limited by structural constraints, a behaviour which we formalise by defining symmetric partially-monoidal categories. We reconstruct quantum theory from the global theories of unitary groups acting on projective Hilbert spaces.

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Stefano Gogioso. 2019-05-30. A Process-Theoretic Church of the Larger Hilbert Space. https://arxiv.org/abs/1905.13117

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