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Because $\\partial_\\phi\\rho(\\phi)$ is always Hermitian and traceless, this ratio is constrained more strongly than for a generic operator. For any nonzero tangent operator $X=\\partial_\\phi\\rho$ of rank $r$, we prove the sharp bounds $\\sqrt{2}\\le \\|X\\|_1/\\|X\\|_2\\le \\sqrt r$. 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