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Open Quantum Systems Decoherence

Separable neighbourhood of identity in C^ast-algebras

arXiv

Authors: Mizanur Rahaman, Mateusz Wasilewski

Year

2026

Paper ID

38939

Status

Preprint

Abstract Read

~2 min

Abstract Words

105

Citations

N/A

Abstract

We study the structure of separable elements in bipartite C^ast-algebras, focusing on the existence and size of a separable neighbourhood around the identity element. While this phenomenon is well understood in the finite-dimensional setting, its extension to general C^ast-algebras presents additional challenges. We show that the problem of determining such a neighbourhood can be reduced to estimating the completely bounded norm of contractive positive maps. This approach allows us to characterize the size of such neighbourhoods in terms of structural properties of the algebra, notably its rank. As a consequence, we also resolve a recent conjecture of Musat and Rørdam.

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We study the structure of separable elements in bipartite C^ast-algebras, focusing on the existence and size of a separable neighbourhood around the identity element.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.29556 [2] arXiv https://arxiv.org/abs/2603.29556 [3] Publisher https://arxiv.org/abs/2603.29556

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