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Paper 1
Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes.
Chen J, Fang W, Zhou S, Qiu J, Zhang C, Xu Y, Zeng B, Chen Y.
- Year
- 2023
- Journal
- Entropy (Basel)
- DOI
- 10.3390/e25121603
- arXiv
- -
No abstract.
Open paperPaper 2
Essential Duality and Maximal Non-signalling Extensions in Algebraic Quantum Field Theory
Hassan Nasreddine
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2605.00075
- arXiv
- 2605.00075
We show that, under additivity, the maximal von Neumann algebra extension of $\mathcal{A}(O)$ inside $B(\mathcal{H})$ whose inner automorphisms are non-signalling with respect to all spacelike-separated regions is $\mathcal{A}(O')'$. Consequently, $\mathcal{A}(O)$ is maximal with respect to this property if and only if essential duality holds. The proof is purely algebraic. When essential duality fails, we construct a proper extension all of whose inner automorphisms, and more generally all normal completely positive maps admitting Kraus operators in the algebra, are non-signalling. Under essential duality, any proper extension necessarily admits a signalling operation. An entropic formulation using Araki relative entropy provides a quantitative diagnostic of signalling, though it is not used in the proof. Additional structural results include the wedge-intersection identity $\mathcal{A}(O')' = \bigcap_{W \supset O}\mathcal{A}(W)$ and equivalent characterisations of essential duality. These results identify essential duality as an operational maximality condition within the given representation.
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