= Solution
<Quantum teleportation> transfers an arbitrary unknown <qubit> state to a separated receiver while using <local operations and classical communication>, rather than sending that input qubit. Alice and Bob first share one <maximally entangled state> of two qubits, such as a <Bell pair>; a shared <spin singlet state> is equivalent after a known <local unitary operation>.
Alice performs a joint <Bell-basis measurement> on the input qubit and her half of the pair. There are four possible outcomes. Bob's conditional qubit is the input state transformed by a known <Pauli operator> determined by that outcome. Alice sends the outcome as two classical bits, and Bob applies the inverse <Pauli operator>. Thus \b[one shared Bell pair and two classical bits, together with local measurement and correction, transmit one unknown qubit exactly]. The entangled resource is consumed.
The procedure does not produce a classical description of the unknown amplitudes and does not leave a second copy at Alice, so it respects the <no-cloning theorem>. Before receiving the classical outcome, Bob's <reduced density matrix> is $I/2$, independent of the input; this respects the <no-communication theorem>. The next part proves the full identity-channel action, including inputs entangled with another system.
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