I have a quantum circuit with $N$ qubits represented by the unitary $U$. The initial state is $| 00...0\rangle$ and $\psi=U|00...0\rangle$.
Given $\langle\psi| Z_1...Z_{N} |\psi\rangle$ and $\langle \psi|Z_i |\psi\rangle$ $\forall i$, is there a way to find the expectation value $\langle \psi|Z_1...Z_{N-1} |\psi\rangle$?