⚛ Unit I · Fundamentals

Test Your Quantum Knowledge

5 questions covering Qubits, Bloch Sphere, Measurement, Dirac Notation, and Entanglement. Wrong answers come with explanations.

❓ 5 Questions 🏆 20 Marks Each 📊 Total: 100 Marks

Qubits & Superposition

A qubit is in the state |ψ⟩ = (3/5)|0⟩ + (4/5)|1⟩. What is the probability of measuring the qubit in state |1⟩?

A 3/5 = 0.60 (60%) ✗

B 9/25 = 0.36 (36%) ✗

C 16/25 = 0.64 (64%) ✓

D 4/5 = 0.80 (80%) ✗

The Bloch Sphere

On the Bloch sphere, the state |+⟩ = (|0⟩ + |1⟩)/√2 lies at which location?

A The north pole (θ = 0) ✗

B On the equator along the +X axis (θ = π/2, φ = 0) ✓

C The south pole (θ = π) ✗

D The center of the sphere ✗

Quantum Measurement

After you measure a qubit that was in superposition and obtain the result "0", what happens if you immediately measure the same qubit again?

A You will always measure "0" again — the state has collapsed to |0⟩ ✓

B You will always measure "1" because the qubit flips after measurement ✗

C The result is random — 50% chance of "0" or "1" each time ✗

D The qubit returns to superposition before the second measurement ✗

Dirac Notation

In Dirac notation, which of the following correctly expresses the inner product of two states |φ⟩ and |ψ⟩, and what does it physically represent?

A |ψ⟩⟨φ| — the outer product, giving the transition probability ✗

B ⟨ψ|φ⟩ — the bra-ket product, representing the energy of state |ψ⟩ ✗

C |φ⟩|ψ⟩ — tensor product of two states in a combined Hilbert space ✗

D ⟨φ|ψ⟩ — a complex number whose squared modulus |⟨φ|ψ⟩|² gives the probability of measuring |φ⟩ given system is in |ψ⟩ ✓

Quantum Entanglement

Two qubits are prepared in the Bell state |Φ⁺⟩ = (|00⟩ + |11⟩)/√2. Qubit A is sent to Hyderabad and Qubit B to New York. If qubit A is measured and collapses to |1⟩, what can we say about qubit B?

A Qubit B is in |0⟩ — opposite state because of conservation laws ✗

B Qubit B instantly collapses to |1⟩ — the same state, due to entanglement ✓

C Qubit B remains in equal superposition since no signal was sent ✗

D Qubit B collapses to a random state unrelated to qubit A ✗

/100

✓ Correct

✗ Wrong

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