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arXiv · 2611.09321

Critical properties of EPR steering

Yu-Xuan Zhang·Jing-Ling Chen
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Abstract

Every PVM-critical entangled two-qubit state becomes steerable with two copies. We prove this for the full critical boundary and for two different critical inputs. The joint measurements can have arbitrarily little entanglement, while all conditional states on Bob's two systems remain separable. Criticality is exactly the point where this measurement-entanglement threshold vanishes. The number of measurements has a separate critical behavior: every fixed setting bound leaves an unsteerable neighborhood of the critical input. Moreover, for any such bound, there are critical states that remain unsteerable under every tensor power, although unrestricted measurements activate them with two copies. These results identify different roles for measurement entanglement, measurement number, and collective access in revealing steering. We also construct fixed-dimensional states whose steering activates on two copies while Bell locality persists through any prescribed finite copy range. In increasing dimension, the two-copy steering violation is unbounded, giving an affirmative solution to the amplification question of Hsieh, Liang, and Lee.

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Yu-Xuan Zhang, Jing-Ling Chen. 2026-11-06. Critical properties of EPR steering. https://arxiv.org/abs/2611.09321

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