= Relativistic causality constraint on an ideal nonlocal measurement
The nonselective channel of a hypothetical spacelike nonlocal <quantum measurement> must not allow a distant input change to alter local output statistics. For a rank-one measurement in the rotated even and odd two-qubit bases with angle $\theta$, Alice's output satisfies
$$
\langle Z_A\rangle_{\rm out}=\cos^2(2\theta)\langle Z_A\rangle_{\rm in}+\sin2\theta\cos2\theta\langle X_AX_B\rangle_{\rm in}.
$$
Bob can change the last correlation using only his local <Pauli Z gate> while Alice keeps the input $|+\rangle$. The resulting signal excludes $0<\theta<\pi/4$. Degenerate observables that do not distinguish this basis are not covered by the rank-one argument. Locally recording a jointly encoded result, which is decoded later by <local operations and classical communication>, is compatible with <quantum no-signalling>.
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