Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 15E / b

Charlie measures in the $X$ basis and sends one bit to Alice or Bob; the remaining pair becomes $|{\Phi }^{+}⟩$ or $|{\Phi }^{-}⟩$, corrected by a local $Z$. Alice then performs standard teleportation: CNOT from $|\xi ⟩$ to her GHZ qubit, Hadamard, two computational measurements, and sends the two outcomes to Bob, who applies the corresponding Pauli correction.

No. Without classical communication Bob's reduced state is independent of Alice's unknown input by no-signalling, whereas successful transfer would make it equal to that input.