= Primitive quantum channel
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A finite-dimensional <quantum channel> is primitive when some power maps every nonzero positive semidefinite operator to a positive-definite operator. Repeated application then forgets the initial state and approaches a unique stationary <density operator> with full rank.
An equivalent spectral criterion requires a full-rank stationary state, a simple eigenvalue one and no other eigenvalue on the unit circle. The full-rank condition is essential: an <amplitude damping channel> can have a unique stationary pure ground state and all other eigenvalues inside the unit circle without being primitive. A state starting in that ground state never becomes positive definite. Primitivity is therefore stronger than merely having a unique attractive stationary state, and its use in relaxation arguments must specify the finite-dimensional setting.
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