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We prove that many spectral lower bounds for the chromatic number, $\\chi$, are also lower bounds for $\\xi$. This result complements a previous result by the authors, in which they showed that spectral lower bounds for $\\chi$ are also lower bounds for the quantum chromatic number $\\chi_q$. 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We prove that many spectral lower bounds for the chromatic number, $\\chi$, are also lower bounds for $\\xi$. This result complements a previous result by the authors, in which they showed that spectral lower bounds for $\\chi$ are also lower bounds for the quantum chromatic number $\\chi_q$. 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