The most general formula of Kraus operator on density matrix is:
$$\rho\to \sum_k A_k^\dagger\rho A_k.$$ If I want to write this equation for one qubit, the most general way will be:
$\rho_f = (a^*I+b^*X+c^*Y+d^*Z)\rho(aI+bX+cY+dZ)$ Thanks to @Quantum Mechanic, the formula should be
$∑k(a_k^∗I+b_k^∗X+c_k^∗Y+d_k^∗Z)ρ(a_kI+b_kX+c_kY+d_kZ)$
Now, I want to write it for n qubit. (For 2 and 3 qubit and then generalized it)
How to write these equation for 2, 3 and multi qubits?