A class of Bell diagonal entanglement witnesses in $\mathbb{C}^4 \otimes \mathbb{C}^4$: optimization and the spanning property

• URL: http://arxiv.org/abs/2112.15183v1
• Date: Thu, 30 Dec 2021 19:22:58 GMT
• Title: A class of Bell diagonal entanglement witnesses in $\mathbb{C}^4 \otimes \mathbb{C}^4$: optimization and the spanning property
• Authors: Anindita Bera, Filip A. Wudarski, Gniewomir Sarbicki, Dariusz Chru\'sci\'nski
• Abstract summary: Two classes of diagonal indecomposable entanglement witnesses in $mathbbC4 otimes mathbbC4$ are considered. We find a generalization of the well-known Choi witness from $mathbbC3 otimes mathbbC3$, while the second one contains the reduction map.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Two classes of Bell diagonal indecomposable entanglement witnesses in $\mathbb{C}^4 \otimes \mathbb{C}^4$ are considered. Within the first class, we find a generalization of the well-known Choi witness from $\mathbb{C}^3 \otimes \mathbb{C}^3$, while the second one contains the reduction map. Interestingly, contrary to $\mathbb{C}^3 \otimes \mathbb{C}^3$ case, the generalized Choi witnesses are no longer optimal. We perform an optimization procedure of finding spanning vectors, that eventually gives rise to optimal witnesses. Operators from the second class turn out to be optimal, however, without the spanning property. This analysis sheds a new light into the intricate structure of optimal entanglement witnesses.

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