Qubit teleportation procedure

The teleportation procedure has input a normalized qubit vector $\mathrm{\mid }\psi {⟩}_A\in Q_2$ and a preshared resource $\mathrm{\mid }{\mathrm{\Phi }}^{+}{⟩}_{BC}$, with Alice holding wires $A,B$ and Bob holding $C$. The wire order is $A,B,C$. It uses $\mathrm{\mid }{\mathrm{\Phi }}^{+}⟩$ from The Bell vectors, CNOT with $A$ control and $B$ target from CNOT and Control-Target Order, the Hadamard $H$ from Exact one-qubit gates and rotations, the Pauli matrices from The Pauli matrices, and the finite projective measurement convention of Finite projective measurements.

1. Alice applies ${\mathrm{CNOT}}_{A\to B}$ and then $H_A$, so the combined operator is $V_{AB}=(H_A\otimes I_{BC}){\mathrm{CNOT}}_{A\to B}$, with the rightmost gate applied first.
2. Alice measures $A,B$ in their ordered computational basis and records the pair $(a,b)\in \{0,1{\}}^2$, in that wire order.
3. Alice sends the two classical bits $a,b$ to Bob.
4. Bob applies $X_C^b$ and then $Z_C^a$, whose operator product is $Z_C^a{X}_C^b$.

The output is the corrected state on Bob's wire $C$. The shared Bell pair is an input resource; its preparation and physical realization are outside this procedure. A zero-probability measurement label has no conditional state and is assigned no branch output; the normalized-input hypotheses here are later shown to make all four labels positive.