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arXiv · 2404.16004

Channel-State duality with centers

Simon Langenscheidt·Eugenia Colafranceschi·Daniele Oriti
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Abstract

We study extensions of the mappings arising in usual channel-state duality to the case of Hilbert spaces with a direct sum structure. This setting arises in representations of algebras with centers, which are commonly associated with constraints, and it has many physical applications from quantum many-body theory to holography and quantum gravity. We establish that there is a general relationship between non-separability of the state and the isometric properties of the induced channel. We also provide a generalisation of our approach to algebras of trace-class operators on infinite dimensional Hilbert spaces.

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Simon Langenscheidt, Eugenia Colafranceschi, Daniele Oriti. 2024-04-24. Channel-State duality with centers. https://arxiv.org/abs/2404.16004

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