What is Quantum Decoherence?

 Quantum decoherence is the phenomenon by which classical physics emerges from quantum states and classical probabilities emerge from quantum superpositions. Basically, quantum decoherence is when a quantum system evolves from a pure state to a local mixed state due to entanglement with an external environment.

It seems to me that there are different types of decoherence:

- weak vs medium vs strong: weak decoherence is evolution of the system from a pure state to any mixed state (upon tracing out the environmental degrees of freedom from the global density matrix); whereas strong decoherence is when the mixed state is specifically that where the reduced density matrix's eigenstates and eigenvalues match the outcomes implied by the system's initial superposition i.e., the environmental degrees of freedom constitute a measuring apparatus that match the operator of the superposition eigenbasis and the global evolution maintains convergence to the probabilities implied by the original coefficients. Medium decoherence is when the reduced density matrix's eigenstates match those of the superposition basis as indicated by the off-diagonal terms vanishing, but the probability eigenvalues on the diagonal need not be the initial superposition coefficients' modulus squared.

- natural vs unnatural: natural decoherence is when this local evolution to a mixed state is induced by a fully hermitian global Hamiltonian and associated global unitary time evolution; unnatural decoherence is when the global Hamiltonian contains a non-Hermitian piece and the global time evolution is itself non-unitary.

My sense is the literature typically means weak/medium natural decoherence by decoherence. For example, the Lindblad equation is often used to describe the evolution of the system density matrix to a mixed state. The key point is that the standard system Hamiltonian commutator is insufficient to describe the system's time evolution due to interaction with the environment. The fact that we are taking a local (system) view means we are losing information about the global state and this introduces an additional dissipative term with locally non-unitary dynamics that leads the system to a mixed state.

References:

Open quantum system - Wikipedia
Quantum decoherence - Wikipedia