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In quantum information theory, the proper cones of interest are those generated by density operators, yielding the familiar notion of a separable state. The dual of the cone of separable states is cones of block-positive operators, wherein one finds the entanglement witnesses studied in quantum theory.

At present there is considerable interest in returning to the abstract ideas put forward by Nakioma and Phelps, and the long-standing open problem characterising the context in which the separable cone and its dual coincide has only recently been resolved. In this lecture, I explain some of my own investigations into tensor cones arising from the tensor product of Toeplitz and Fejer-Riesz operator systems.

# Department Colloquium

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Fri., Nov. 3, 2023 3:30 p.m.
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Location: RIC 209
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**Speaker:** Doug Farenick, University of Regina

**Title: **Bipartite entanglement in tensor cones of Toeplitz and Fejer-Riesz operator systems (88 kB)

**Abstract: **

In quantum information theory, the proper cones of interest are those generated by density operators, yielding the familiar notion of a separable state. The dual of the cone of separable states is cones of block-positive operators, wherein one finds the entanglement witnesses studied in quantum theory.

At present there is considerable interest in returning to the abstract ideas put forward by Nakioma and Phelps, and the long-standing open problem characterising the context in which the separable cone and its dual coincide has only recently been resolved. In this lecture, I explain some of my own investigations into tensor cones arising from the tensor product of Toeplitz and Fejer-Riesz operator systems.