Impossible measurements revisited

It is by now well-recognised that the na\"ive application of projection postulate on composite quantum systems can induce signalling between their constituent components, indicative a breakdown causality in relativistic spacetime context. Here we introduce necessary and sufficient condition for an ideal measurement observable to be non-signalling. As well as being particularly simple, it generalises previous no-signalling conditions allows degeneracies applied all bounded self-adjoint operators. The used establish arbitrary sums local observables will not signal, accordance with our expectations from field theory. On other hand, shown tensor product commuting observables, example bipartite operators form $A\otimes B$, fact contrary widely-held belief such measurements are always locally realisable. implications notion theory addressed; appears most straightforward standard formalism generically leads violations causality. We conclude either class measured should restricted and/or translation framework theory, particular postulate, re-evaluated.