Self-Assessment Quiz: Quantum Teleportation

Twenty questions on the teleportation protocol, its resource requirements, what it does and does not transmit, and its role as a primitive. Aim for 16+.

Question 1

Teleporting one qubit consumes:

A) One entangled pair and two classical bits B) Two entangled pairs and one classical bit C) One classical bit only D) Nothing — it is free

Question 2

The classical bits are needed because:

A) They carry the quantum state B) Alice's Bell measurement has four equally likely outcomes and Bob must know which C) They synchronize clocks D) They are optional

Question 3

Before the classical bits arrive, Bob's qubit is:

A) Already in the teleported state B) Maximally mixed — it carries no information C) In state $|0\rangle$ D) Entangled with Alice's measured qubit

Question 4

This is required by:

A) The uncertainty principle B) The no-signalling theorem C) The no-cloning theorem D) Conservation of energy

Question 5

After teleportation, the original qubit at Alice's location is:

A) Unchanged B) Destroyed (projected by the Bell measurement) C) Duplicated D) Entangled with Bob's

Question 6

That destruction is required by:

A) No-cloning B) No-signalling C) Unitarity alone D) Thermodynamics

Question 7

Alice's measurement in the protocol is:

A) A computational-basis measurement B) A Bell-basis measurement on her two qubits C) An $X$-basis measurement D) No measurement is needed

Question 8

Bob's correction for the outcome $10$ is typically:

A) $I$ B) $X$ C) $Z$ D) $XZ$

Question 9

Teleportation transmits information faster than light:

A) Yes B) No — the classical channel is limited by light speed C) Only for entangled senders D) Only over fibre

Question 10

Teleportation requires knowing the state being teleported:

A) Yes B) No — it works on unknown states, which is the point C) Only its basis D) Only its phase

Question 11

The entangled pair must be distributed:

A) After the teleportation B) In advance, before the unknown state arrives C) Simultaneously D) It is not needed

Question 12

Entanglement swapping is:

A) Teleporting one half of an entangled pair, entangling two parties who never interacted B) Exchanging two qubits C) A classical protocol D) Impossible

Question 13

Gate teleportation is used in fault tolerance to:

A) Reduce qubit count B) Apply hard gates (e.g. $T$) using prepared resource states C) Eliminate measurement D) Increase gate error

Question 14

Teleportation fidelity above what threshold cannot be achieved by any classical strategy on an unknown qubit?

A) 1/2 B) 2/3 C) 3/4 D) 1

Question 15

The teleportation circuit's classical control can be removed by:

A) The deferred measurement principle B) Removing the entangled pair C) Measuring in the $X$ basis D) It cannot

Question 16

True or false: Teleportation copies a quantum state.

Question 17

True or false: Teleportation could be used to build a faster-than-light telephone if the classical channel were fast enough.

Question 18

True or false: Teleportation is a routing primitive inside quantum computers, not just a communication protocol.

Question 19

Short answer. Explain why teleportation is consistent with the no-cloning theorem.

Question 20

Short answer. A colleague measures teleportation fidelity of 0.71 and claims success. Is that claim defensible?

Answer Key

Q Ans Note
1 A One ebit + two classical bits per qubit teleported.
2 B The Bell measurement yields one of four outcomes uniformly; without knowing which, Bob cannot pick the right correction. Two bits label four outcomes.
3 B Bob's reduced state is $I/2$ regardless of the input state, until the classical message arrives.
4 B If Bob's local state depended on Alice's input or measurement, that dependence would be a signal, violating no-signalling.
5 B The Bell measurement projects Alice's qubits, destroying the original.
6 A If the original survived alongside Bob's copy, you would have cloned an unknown state.
7 B Implemented as CNOT then $H$, followed by computational-basis measurement.
8 C Conventionally the first bit selects $Z$ and the second selects $X$; conventions vary, so verify against your own circuit rather than memorizing.
9 B The protocol is useless until two classical bits arrive over an ordinary channel.
10 B Teleportation works on arbitrary unknown states — including halves of entangled pairs. If you knew the state you would just describe it classically.
11 B Entanglement is a pre-shared resource, consumed by the protocol.
12 A The basis of quantum repeaters: extend entanglement beyond the range of direct transmission.
13 B $T$ gates are applied by consuming distilled magic states via gate teleportation (Ch. 25) — the standard fault-tolerant route to non-Clifford gates.
14 B The classical limit for teleporting an unknown qubit is 2/3; exceeding it certifies genuinely quantum transmission.
15 A Replace the classically controlled corrections with quantum-controlled gates and defer measurement to the end (Ch. 4).
16 False The original is destroyed. It is a transfer, not a copy — the name is unfortunate.
17 False The classical channel is a channel like any other and obeys relativity. Nothing in the protocol removes it.
18 True On-chip, teleportation moves quantum information between distant regions without SWAP chains, and it is central to how magic states are consumed in fault-tolerant architectures.
19 — Cloning requires two copies to coexist. In teleportation, Alice's Bell measurement destroys her copy at the moment Bob's is created, so there is never a time at which two copies exist. The protocol transfers rather than duplicates, and no-cloning is respected precisely because the original must be destroyed.
20 — Partly. 0.71 exceeds the classical bound of 2/3 ≈ 0.667, so the transmission cannot be explained by a classical measure-and-resend strategy — a real result. But it is far from unit fidelity, and the claim needs an error bar: with a modest number of shots, 0.71 may not be statistically distinguishable from 0.667. The defensible statement is "fidelity 0.71 ± σ, exceeding the classical bound by N σ," with the state and shot count specified.