The Minimal Dimension of Entangled-Noise Advantage
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.
Related
- Quantum Advantage in Multiple Access Wiretap Channels with Entangled Transmitters
- Advantage of Entangled Learning Rules in Quantum Measurement Class Learning
- All Bell inequalities with a quantum advantage in the minimal scenario are self-testing
- Absolutely Maximally Entangled States of 2q Parties in Every Odd Prime-Power Dimension q
- Compressive microendoscopy in the presence of noise and misalignment: the translational correlation advantage of graded-index fibers
BibTeX
@misc{wang2026minimal,
title = {{The Minimal Dimension of Entangled-Noise Advantage}},
author = {Xiao-Ke Wang and Zi-Yuan Liu and Ming-Yang Li and Shengjun Wu and Zeng-Bing Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28367},
eprint = {2609.28367},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28367},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The Minimal Dimension of Entangled-Noise Advantage
AU - Xiao-Ke Wang
AU - Zi-Yuan Liu
AU - Ming-Yang Li
AU - Shengjun Wu
AU - Zeng-Bing Chen
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28367
UR - https://arxiv.org/abs/2609.28367
AB - 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.
ER -