Abstract
In this paper, we delve into a nuanced aspect of the distillability problem within the realm of entanglement theory, specifically examining the distillability of anti-diagonal [Formula: see text] entangled Werner states under the framework of local operations and classical communication (LOCC). To address this, we scrutinize a conjecture central to the distillability issue, initially focusing on its implications in 4-dimensional and 5-dimensional contexts. Through rigorous calculations, we establish that these cases align with the conjecture. Subsequently, we broaden our investigation to encompass [Formula: see text] matrices, demonstrating that both even and odd n-dimensional anti-diagonal matrices are in concordance with the conjecture, thus contributing to a deeper understanding of the distillability problem in quantum entanglement.
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