GHZ-W Genuinely Entangled Subspace Verification with Adaptive Local Measurements

2024/12/27 by Zheng, Congcong, Xu, Ping, Wang, Kun +1 · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2412.19540

Abstract

Genuinely entangled subspaces (GESs) are valuable resources in quantum information science. Among these, the three-qubit GHZ-W GES, spanned by the three-qubit Greenberger-Horne-Zeilinger (GHZ) and W states, is a universal and crucial entangled subspace resource for three-qubit systems. In this work, we develop two adaptive verification strategies, the XZ strategy and the rotation strategy, for the three-qubit GHZ-W GES using local measurements and one-way classical communication. These strategies are experimentally feasible, efficient and possess a concise analytical expression for the sample complexity of the rotation strategy, which scales approximately as 2.248ε^-1lnδ^-1, where ε is the infidelity and 1-δ is the confidence level. Furthermore, we comprehensively analyze the two-dimensional two-qubit subspaces and classify them into three distinct types, which include unverifiable entangled subspaces, revealing intrinsic limitations in local verification of entangled subspaces.

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