Bad Qubits — Learn Quantum by Doing

Multiple choice

In the canonical decoherence model, a system qubit

\alpha|0\rangle + \beta|1\rangle

becomes entangled with an environment so the reduced density matrix

\rho_S

has off-diagonal coherences multiplied by the decoherence factor

D = \langle e_0|e_1\rangle

. What happens to

\rho_S

when the two branches drive the environment into orthogonal states (

D = 0

The coherences vanish entirely and $\rho_S$ becomes the incoherent classical mixture $\mathrm{diag}(|\alpha|^2, |\beta|^2)$
Nothing changes; the qubit remains in its original coherent superposition
The populations $|\alpha|^2$ and $|\beta|^2$ are erased while the coherences survive
$\rho_S$ becomes a pure state with enhanced off-diagonal terms