Bad Qubits — Learn Quantum by Doing

Multiple choice

The classically-correlated separable state (1/2)|00><00| + (1/2)|11><11| has reduced-state entropy S(rho_A) = 1 bit. Why is S(rho_A) nevertheless NOT a valid entanglement measure for mixed states?

S(rho_A) is not defined for mixed states, only for pure states
S(rho_A) increases under LOCC for this state, violating monotonicity
S(rho_A) is always zero for separable states, so the value 1 must be a computational error
This state is separable and contains zero entanglement, yet S(rho_A) = 1 bit, so the reduced entropy mixes genuine entanglement with mere classical correlation