= Maximally mixed state
{title2=$\rho_*=I_N/N$}
The maximally mixed <density operator> on an $N$-dimensional <Hilbert space> assigns equal weights to every vector of any <orthonormal basis>. It is invariant under every <unitary operator>. Its purity is $\operatorname{Tr}(\rho_*^2)=1/N$, the minimum possible because the nonnegative <eigenvalues> sum to one and obey the <Cauchy-Schwarz inequality>. For $N>1$ it is a <mixed state>; for $N=1$ it is the sole pure state. A rank-$k$ projector has probability $k/N$ in this state.
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