= Spectral majorization under a unital quantum channel
{title2=$\lambda(\Lambda(\rho))\prec\lambda(\rho)$}
A <unital quantum channel> mixes its input spectrum with a <doubly stochastic matrix>, so its output spectrum satisfies the <majorization> relation with its input spectrum. The reverse inequality is generally false: a <pure state> can be sent to a maximally mixed state. The direction expresses the fact that unital noise can make eigenvalues more uniform. Equality of the two spectra is possible, for example under a unitary channel.
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