= Perfect two-basis discrimination would allow superluminal signalling
Suppose two orthonormal <qubit> bases have disjoint physical rays. Alice chooses which conjugate basis to measure on her half of a <Bell state>. A device that perfectly labels Bob's individual member of either basis would reveal Alice's choice without her outcome being communicated. Spacelike operation would therefore violate relativistic causality, even though ordinary <projective measurements> see the same <reduced density matrix> $I/2$.
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