The maximally mixed state on m qubits is defined to be the quantum state with associated density operator $\rho_m = \frac{1}{2^m} I$. Examples are
- On one qubit this is $\rho_1 = \frac{1}{2}(|0\rangle\langle0|+|1\rangle\langle1|) = \frac{1}{2}I$
- On two qubits we have $\rho_2 = \frac{1}{4} (|00\rangle\langle00| +|01\rangle\langle01|+|10\rangle\langle10|+|11\rangle\langle11|$.
My question is the following: how can the corresponding state vector $|\phi_m\rangle$ be expressed in terms of the standard basis elements, eg. $|\phi_2\rangle = \sum_{i,j} a_{i,j}|ij\rangle$? What are the values of $a_{i,j}$?