 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 satisfiesBob can change the last correlation using only his local Pauli Z gate while Alice keeps the input $|+⟩$. 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.