# Toeplitz separability, entanglement, and complete positivity using operator system duality

@inproceedings{Farenick2022ToeplitzSE, title={Toeplitz separability, entanglement, and complete positivity using operator system duality}, author={Douglas R. Farenick and Michelle McBurney}, year={2022} }

. A new proof is presented of a theorem of L. Gurvits, which states that the cone of positive block-Toeplitz matrices with matrix entries has no entangled elements. We also show that in the cone of positive Toeplitz matrices with Toeplitz entries, entangled elements exist in all dimensions. The proof of the Gurvits separation theorem is achieved by making use of the structure of the operator system dual of the operator system C ( S 1 ) ( n ) of n × n Toeplitz matrices over the complex ﬁeld, and…

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