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Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations

Categorical relations and bipartite entanglement in tensor cones for Toeplitz and Fejér-Riesz operator systems

arXiv
Authors: Douglas Farenick

Year

2023

Paper ID

52915

Status

Preprint

Abstract Read

~2 min

Abstract Words

116

Citations

N/A

Abstract

The present paper aims to understand separability and entanglement in tensor cones, in the sense of Namioka and Phelps, that arise from the base cones of operator system tensor products. Of particular interest here are the Toeplitz and Fejér-Riesz operator systems, which are, respectively, operator systems of Toeplitz matrices and Laurent polynomials of bounded degree (that is, trigonometric polynomials), and which are related in the operator system category through duality. Some additional categorical relationships established in this paper for Toeplitz and Fejér-Riesz operator systems. Of independent interest is a single matrix criterion, similar to the criterion involving the Choi matrix, for a linear map of the Fejér-Riesz operator system to be completely positive.

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  • The present paper aims to understand separability and entanglement in tensor cones, in the sense of Namioka and Phelps, that arise from the base cones of operator system tensor...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2312.01462 [2] arXiv https://arxiv.org/abs/2312.01462 [3] Publisher https://arxiv.org/abs/2312.01462

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