Moreover, the expectation value of any permutaionally invariant operator is the same for ϱ ϱ and for ϱ ϱ P I . Very relevant examples of such operators are projectors to symmetric states, such as the Greenberger–Horne–Zeilinger state, the W state and symmetric Dicke states. Thus, we can obtain the fidelity with respect to the above-mentioned quantum states as the expectation value of the corresponding projectors in the state ϱ ϱ P I .