This note is part of [[quantum/Practical Quantum Information System]]. > [!info] Course code > Use the companion repository for this lecture's runnable lab, helper functions, and regression checks: > - [notebooks/by_concept/quantum_teleportation.ipynb](https://github.com/montekkundan/quantum-code/blob/main/notebooks/by_concept/quantum_teleportation.ipynb) > - [qcourse/protocols.py](https://github.com/montekkundan/quantum-code/blob/main/qcourse/protocols.py) > - [tests/test_protocols_algorithms_qec.py](https://github.com/montekkundan/quantum-code/blob/main/tests/test_protocols_algorithms_qec.py) [TODO: add video - Quantum Teleportation] ## What This Concept Is Quantum teleportation sounds dramatic, but its real lesson is precise: an unknown quantum state can be transferred from one location to another without being copied or physically carried as a statevector through space. The cost is shared entanglement plus classical communication. This protocol is valuable because it forces you to hold several ideas together at once: Bell states, measurement, conditional correction, and the no-cloning constraint. If you understand teleportation properly, many later distributed and networked quantum ideas become easier to read. ## Foundation Terms You Need First A [[quantum/Glossary#Bell state|Bell state]] is the shared entangled resource. [[quantum/Glossary#Teleportation|Teleportation]] uses that shared resource plus two classical bits. The [[quantum/Glossary#No-cloning theorem|no-cloning theorem]] tells you why teleportation cannot be interpreted as "copying the original state to a second place." Keep one structural fact clear: the classical bits do not describe the full unknown state. They only tell the receiver which correction to apply because the entangled pair already supplied the quantum resource. ## How The Idea Actually Works Alice starts with an unknown input state and one half of an entangled Bell pair. Bob holds the other half. Alice performs a Bell-basis measurement on the input qubit together with her Bell-pair qubit. That measurement produces two classical bits. Those classical bits are sent to Bob. Depending on the outcome, Bob applies one of a small set of correction gates. After the correction, Bob's qubit is in the original input state. The protocol does not violate no-cloning because Alice's Bell-basis measurement destroys the original standalone description. It also does not enable faster-than-light signalling because Bob cannot recover the state until the classical bits arrive. The deepest lesson is that "quantum information transfer" and "physical particle transport" are not the same thing. What is transferred operationally is the state assignment, and the transfer is made possible by combining pre-shared entanglement with classical coordination. ## Why It Matters - It is one of the clearest demonstrations that entanglement is a communication resource. - It trains you to track which parts of a protocol are quantum and which parts are classical. - It prepares you for entanglement swapping, repeaters, and distributed quantum systems. ## Study Checks Use these after the explanation, not before it. ### Quick Checks - What resource does teleportation consume? **Answer:** One shared Bell pair and two classical bits of communication. - MCQ: Does teleportation copy the unknown input state? A. Yes B. No C. Only if the state is entangled D. Only on a simulator **Answer:** B. No. ### Oral Exam Anchors > [!question] Oral exam anchor > Explain quantum teleportation as a resource transformation. A good answer should say: Quantum teleportation transfers an unknown quantum state from Alice to Bob using one shared Bell pair and two classical bits. Alice performs a Bell-basis measurement on the unknown state and her half of the Bell pair. This produces two classical bits. She sends those bits to Bob. Bob applies the corresponding Pauli correction to his half of the Bell pair and recovers the original unknown state. The protocol does not copy the state. Alice's measurement destroys the original local copy, and Bob's corrected qubit becomes the output. Teleportation is therefore a resource transformation: shared entanglement plus classical communication can transmit an unknown quantum state without sending the physical qubit that originally carried it. ## Practical Lab Run the protocol with explicit correction logic so the classical side remains visible. - Prepare an arbitrary one-qubit input state to teleport. - Implement Bell-pair sharing, Bell-basis measurement, and the conditional correction operations. - Verify in simulation that the recovered state matches the input state after the correction step. ## Homework Use the homework to separate what is quantum from what is classical in the protocol. - Explain why teleportation does not violate no-cloning. - Explain why teleportation does not enable faster-than-light communication. - Derive the correction rule that maps Alice's two classical bits to Bob's gate choice. ## References - Scott Aaronson, [Introduction to Quantum Information Science](https://www.scottaaronson.com/qclec.pdf), Lecture 10. - IBM Quantum Learning, [learning portal](https://quantum.cloud.ibm.com/learning/en). - Qiskit documentation, [main docs](https://qiskit.org/documentation/).