Channel-State duality with centers

TL;DR

This paper extends the channel-state duality framework to Hilbert spaces with centers, relevant for constrained quantum systems, and explores the relationship between state separability and channel properties.

Contribution

It generalizes channel-state duality to algebras with centers and infinite-dimensional spaces, with applications in quantum physics and gravity.

Findings

Relationship between non-separability and channel isometry established.

Generalization to infinite-dimensional trace-class operator algebras.

Applicable to quantum many-body systems, holography, and quantum gravity.

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.