Entanglement: Bell and GHZ States

Intermediate Quantum Entanglement

Created by Pavel · 11.03.2026 at 14:32 UTC

Entangled states are not products of separate qubit states: the vector lives in the joint space, so correlations can be stronger than shared classical randomness alone. Bell and GHZ templates—Hadamard plus CNOT fan-out—are the usual starting points.

More entangling depth is not always better; noise accumulates, so hardware-aware layout matters as much as circuit diagrams. [1], [2].

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Tasks

Question 1

Which circuit fragment is canonical for creating a Bell state from |00>?

Hint

Create superposition first, then correlate.

X on q0, then X on q1

H on q0, then CNOT q0->q1

Z on q0, then H on q1

CNOT q1->q0 only

Question 2

In a Bell state, a single-qubit measurement outcome is typically:

Hint

Local vs joint behavior.

Deterministic always 0

Deterministic always 1

Random locally, but correlated jointly

Undefined

Question 3

How many basis terms appear in the ideal 3-qubit GHZ superposition?

Hint

Only all-zeros and all-ones terms.

Question 4

Which pair best distinguishes entanglement from simple classical correlation?

Hint

Look for separability/coherence language.

Entanglement requires phase-coherent non-separable state structure

Classical correlation cannot exist in probability theory

Entanglement is only a naming convention

Classical and quantum correlations are always identical

Question 5

Provide the two computational-basis strings that define GHZ(3).

Hint

All equal bits.

000 and 111

none of the above

all of the above

insufficient information

Question 6

In an ideal Bell state $\frac{|00\rangle + |11\rangle}{\sqrt{2}}$, what is $P(\text{two measurements are equal})$?

Hint

Only 00 and 11 appear.

Question 7

Which statement best captures why Bell-state correlations are non-classical?

Hint

Focus on separability and coherence.

They are stronger than any logically possible classical model

They arise from non-separable coherent state structure, not just shared randomness

They imply each qubit has deterministic local outcomes

They require no quantum gates to prepare

Question 8

In noisy hardware, which change most directly threatens useful entanglement in deep circuits?

Hint

Depth and coherence time trade off.

Reducing CNOT count

Increasing decoherence exposure with unnecessary depth

Using fewer shots

Renaming qubits

Question 9

Implement bell_correlation_probability() -> float returning the ideal probability that two Z-measurements on the Bell state $(|00\rangle+|11\rangle)/\sqrt2$ agree (both 00 or both 11).

Hint

Only 00 and 11 have amplitude; they are mutually exclusive.

def bell_correlation_probability() -> float:
    # TODO: return probability two independent Z measurements match
    pass

Starter code is prefilled; replace TODO blocks with your solution.

Runtime output (stdout/stderr)

2 test cases will be used for grading

Run checks runtime behavior only. Final correctness is evaluated when you submit.

Card Info

Topic: Quantum Entanglement
Difficulty: Intermediate
Completed: 0 users

Creator

Pavel