Bad Qubits — Learn Quantum by Doing

Multiple choice

Let P be the projector onto a quantum code's codespace and {E_a} be a set of error operators. According to the Knill-Laflamme conditions, a recovery operation that perfectly corrects every error in {E_a} exists if and only if which relation holds for all a, b?

P E_a^dagger E_b P = 0 for all a and b, with no exceptions
E_a^dagger E_b = alpha_ab I on the entire 2^n-dimensional Hilbert space
P E_a^dagger E_b P = alpha_ab P, where alpha_ab is a Hermitian matrix of scalars independent of the codeword
P E_a P = P E_b P for every pair of errors a and b