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arXiv · 2609.28367

The Minimal Dimension of Entangled-Noise Advantage

Xiao-Ke Wang·Zi-Yuan Liu·Ming-Yang Li·Shengjun Wu·Zeng-Bing Chen
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Abstract

Can entangled noise erase entanglement more efficiently than separable noise? Standard robustness restricts the added noise to separable states; generalized robustness allows any state. We prove that the two costs coincide for every two-qubit state and give an explicit full-rank qubit--qutrit state with a strict gap. Positivity under partial transpose (PPT) characterizes separability in both dimensions, so the boundary is not caused by a failure of the PPT criterion. Instead, product-vector geometry permits a rank-one bridge between the two-qubit dual optimizations and supplies a two-dimensional completely entangled subspace for the qubit--qutrit separation. Local isometric embeddings complete the finite-dimensional bipartite classification, also for any fixed multipartite cut. Combined with known three-qubit separation, the result classifies universal equality relative to full separability in all finite multipartite systems.

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Xiao-Ke Wang, Zi-Yuan Liu, Ming-Yang Li, Shengjun Wu, Zeng-Bing Chen. 2026-09-23. The Minimal Dimension of Entangled-Noise Advantage. https://arxiv.org/abs/2609.28367

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