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This research establishes precise mathematical thresholds for entanglement in noisy Greenberger-Horne-Zeilinger systems, proving that observed quantum eraser data requires a specific minimum level of entanglement rather than assuming its presence. By deriving exact separability conditions and lower bounds through semidefinite programming, the study provides rigorous tools to distinguish genuine multipartite correlations from those explainable by classical assumptions in experimental setups.
Measurement records reveal the entanglement needed, not assumed, in a quantum system

This work determines the minimum entanglement compatible with quantum eraser data, distinguishing it from optimal which-path setups.
Mohd Asad Siddiqui, Government Girls P.G. College has demonstrated that recovering interference fringes through a “quantum eraser” does not, by itself, prove entanglement. Researchers established “sharp entanglement-depth thresholds” for noisy Greenberger-Horne-Zeilinger preparations, and developed an “exact semidefinite characterization” to pinpoint when three-qubit data lacks full entanglement at any measurement angle, using mathematically verifiable results. These results establish what entanglement is required by the measurement record, rather than inferred from assumptions about the source. Researchers have established that the compatibility of recorded eraser data with a specific minimum level of entanglement distinguishes it from simply assuming entanglement based on optimal path distinguishability or additional measurement outcomes. This work moves beyond detecting that entanglement exists, to quantifying how much is necessary for a given experimental setup. For noisy Greenberger-Horne-Zeilinger (GHZ)…
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