Quantum teleportation

Teleportation moves an unknown state $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$ from Alice to Bob using one shared Bell pair and two classical bits. Alice holds $|\psi\rangle$ and her half of $\frac{1}{\sqrt2}(|00\rangle+|11\rangle)$; she applies CX then $H$ to the pair and measures both in the computational basis, obtaining classical bits $(m_1,m_2)$. Before measurement the three-qubit state can be written as an equal superposition over Alice's four outcomes, each pairing a Bell-basis result with a specific Pauli acting on Bob's qubit: $\frac{1}{2}\sum_{m_1,m_2}|m_1 m_2\rangle\otimes Z^{m_1}X^{m_2}|\psi\rangle$. Bob applies $X^{m_2}Z^{m_1}$ to undo that Pauli and recovers $|\psi\rangle$ exactly — the ideal-circuit result this record checks on a toy state. No information travels faster than light: Bob's qubit is maximally mixed until the two classical bits arrive, and the protocol consumes (does not clone) the input state, consistent with the no-cloning theorem.