Questions: Quantum Teleportation

Question 1

In quantum teleportation, why are two classical bits of communication required?

• A. To transmit the qubit's amplitude information directly
• B. To tell Bob which of four possible corrective operations to apply based on Alice's Bell measurement outcome
• C. To verify that the teleportation succeeded
• D. To establish the entangled pair between Alice and Bob

Answer: (B)

Alice's Bell measurement has four equally likely outcomes, each corresponding to one of the four Pauli operators {I, X, Z, XZ} that Bob must apply to recover the original state. Two classical bits encode which of the four outcomes occurred. Without this classical message, Bob's qubit is in a completely random state — the entanglement alone does not transmit information.

Question 2

Quantum teleportation allows faster-than-light communication because the state transfer is instantaneous once Alice measures.

• T. True
• F. False

Answer: False

After Alice's measurement, Bob's qubit is in one of four equally likely states, each of which is maximally mixed (completely random) from Bob's perspective. Bob cannot extract any information until he receives Alice's two classical bits, which travel at most at the speed of light. The protocol therefore respects relativistic causality. Entanglement enables correlation, not communication.

Question 3

After teleportation, Alice's original qubit is in the state that was teleported to Bob. True or false, and why?

Model answer: False. Alice's original qubit has been measured as part of the Bell measurement and has collapsed into a Bell basis state. The original state no longer exists at Alice's location — it has been transferred to Bob. This is consistent with the no-cloning theorem: the state was moved, not copied.

Teleportation is fundamentally a state transfer, not a state copy. The Bell measurement at Alice's end irreversibly destroys the input state's coherence, projecting it onto one of four entangled states with her half of the shared pair. The quantum information is gone from Alice's side and reconstructed at Bob's side after correction. If the original survived, we would have two copies of an unknown quantum state, violating the no-cloning theorem.