Bad Qubits — Learn Quantum by Doing

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Quantum trajectory (Monte Carlo wavefunction) methods are computationally attractive because they propagate a pure state vector instead of a density matrix. For a system of n qubits, how do the sizes of these two objects compare?

The state vector has 4^n entries while the density matrix has 2^n entries
The state vector has n entries while the density matrix has n^2 entries
The state vector has 2^n entries while the density matrix has 4^n entries
Both objects have exactly 2^n entries, so there is no size advantage