GHZ-W Genuinely Entangled Subspace Verification with Adaptive Local Measurements

TL;DR

This paper introduces adaptive local measurement strategies to verify the GHZ-W genuinely entangled subspace in three-qubit systems, providing efficient methods and analyzing limitations in local verification.

Contribution

It develops two adaptive verification strategies for GHZ-W GES using local measurements, with analytical sample complexity and classification of two-qubit subspaces.

Findings

Sample complexity scales as approximately 2.248/ε * ln(1/δ)

Strategies are experimentally feasible and efficient

Identifies intrinsic limitations in local verification of entangled subspaces

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 $2.248\epsilon^{-1}\ln\delta^{-1}$, where $\epsilon$ is the infidelity and $1-\delta$ 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.