Self-Assessment Quiz: Superdense Coding and Quantum Key Distribution

Twenty questions on superdense coding, BB84, E91, eavesdropper detection, and what QKD actually guarantees. Aim for 16+.

Question 1

Superdense coding transmits:

A) One classical bit using two qubits B) Two classical bits by sending one qubit, given a pre-shared entangled pair C) Two qubits using one classical bit D) Unlimited information

Question 2

Superdense coding and teleportation are:

A) Unrelated B) Duals — one sends 2 classical bits with 1 qubit + 1 ebit, the other sends 1 qubit with 2 classical bits + 1 ebit C) The same protocol D) Both classical

Question 3

Alice encodes two bits in superdense coding by applying:

A) One of $\{I, X, Z, XZ\}$ to her half of the pair B) A measurement C) A Hadamard only D) Nothing

Question 4

Bob decodes by:

A) Measuring in the computational basis B) Performing a Bell measurement on both qubits C) Applying $H$ only D) Waiting for a classical message

Question 5

Without the pre-shared entanglement, sending one qubit conveys at most:

A) 2 classical bits B) 1 classical bit C) 0 bits D) Unlimited

Question 6

That limit is known as:

A) The Tsirelson bound B) The Holevo bound C) The no-cloning theorem D) Bell's theorem

Question 7

In BB84, Alice sends qubits encoded in:

A) One fixed basis B) One of two randomly chosen conjugate bases ($Z$ or $X$) C) Three bases D) The Bell basis

Question 8

Sifting in BB84 means:

A) Discarding rounds where Alice's and Bob's bases differed B) Error correction C) Amplifying the key D) Measuring twice

Question 9

Roughly what fraction of raw rounds survive sifting?

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

Question 10

An intercept-resend eavesdropper introduces a QBER of approximately:

A) 0% B) 11% C) 25% D) 50%

Question 11

BB84 is typically aborted above a QBER of about:

A) 1% B) 11% C) 25% D) 50%

Question 12

Eve's fundamental obstacle is:

A) She cannot measure qubits B) She cannot copy an unknown state (no-cloning) and measuring in the wrong basis disturbs it C) The classical channel is encrypted D) Photons travel too fast

Question 13

E91 detects eavesdropping by:

A) Checking a Bell/CHSH inequality violation B) Counting photons C) Timing analysis D) Comparing all key bits

Question 14

Privacy amplification is:

A) Increasing laser power B) Compressing a partially-known key into a shorter, nearly-uniform key C) Adding more qubits D) Broadcasting the key

Question 15

QKD protects:

A) Data at rest B) Digital signatures C) Key exchange over a dedicated quantum channel D) Firmware integrity

Question 16

True or false: QKD is unconditionally secure in practice, independent of implementation.

Question 17

True or false: QKD replaces the need for post-quantum cryptography.

Question 18

True or false: Superdense coding violates the Holevo bound.

Question 19

Short answer. Explain why intercept-resend produces 25% QBER, showing the arithmetic.

Question 20

Short answer. A vendor offers QKD to secure a bank's inter-branch traffic across the public internet. Give two technical objections.

Answer Key

Q Ans Note
1 B The pre-shared ebit is what makes it possible; without it, one qubit carries one bit.
2 B The resource accounting is exactly reversed — the cleanest way to see they are two faces of one relationship.
3 A The four Paulis map the shared Bell state onto the four orthogonal Bell states, i.e. two bits.
4 B Because the four possibilities are orthogonal Bell states, a Bell measurement distinguishes them perfectly.
5 B One qubit carries at most one bit of accessible classical information.
6 B The Holevo bound.
7 B $Z$ or $X$, chosen at random per qubit — conjugate bases are what make eavesdropping detectable.
8 A Alice and Bob publicly compare basis choices (not outcomes) and keep only matching rounds.
9 B Bases match half the time on average.
10 C See Q19.
11 B The standard BB84 threshold is ~11% for one-way postprocessing; above it, no secret key can be distilled.
12 B Both halves matter: she cannot clone, and any measurement in the wrong basis randomizes the state.
13 A E91 uses entangled pairs and certifies security by violating a Bell inequality — device-independent in the strongest formulations.
14 B A hash-based compression that removes Eve's partial information at the cost of key length.
15 C Only key exchange, and only over a channel that supports quantum transmission.
16 False The protocol has information-theoretic security proofs; implementations have been broken repeatedly via side channels — detector blinding, photon-number splitting on imperfect sources, timing attacks. Security proofs assume device models that real hardware violates.
17 False QKD addresses key exchange only. It does nothing for digital signatures, certificates, code signing, or data at rest, and it requires dedicated hardware and fibre. PQC is software and covers all of it.
18 False Two qubits are involved in total (one pre-shared, one transmitted), so two bits for two qubits is exactly Holevo-consistent. The pre-shared half was distributed earlier, which is why the protocol needs entanglement in advance.
19 — Eve measures in a random basis. Half the time she picks correctly, resends the right state, and introduces no error. Half the time she picks wrongly, collapsing the state into her basis; the resent qubit is then random relative to Alice's encoding, so when Bob's basis matches Alice's he gets the wrong answer half the time. Total error rate on sifted bits: $\tfrac12 \times 0 + \tfrac12 \times \tfrac12 = 25\%$.
20 — (1) QKD needs a dedicated quantum channel — dark fibre or free-space line of sight — and cannot be routed over the public internet, since routers, amplifiers, and switches destroy quantum states. (2) Range is limited to roughly a few hundred kilometres without trusted nodes or repeaters; trusted-node architectures reintroduce exactly the trust assumption QKD claims to eliminate. Further objections: it secures only key exchange, needs authenticated classical channels anyway (which needs PQC signatures), and costs far more than deploying ML-KEM in software.