Curriculum / Entanglement & Protocols / GHZ States
GHZ States
Create multi-qubit entangled states.
GHZ States
Beyond Two-Qubit Entanglement
Bell states entangle two qubits. But quantum mechanics allows entanglement to spread across any number of particles, and the resulting correlations become stranger, not just larger. The GHZ state (named for Greenberger, Horne, and Zeilinger) is the simplest and most famous example of genuine multipartite entanglement:
|GHZ⟩ = (|000⟩ + |111⟩)/√2
In this state, all three qubits are maximally correlated: measure one in the computational basis and all three collapse simultaneously. If qubit 0 reads 0, qubits 1 and 2 are guaranteed to also be 0. If qubit 0 reads 1, all three are 1. There are no intermediate outcomes.
Creating a GHZ State
The GHZ circuit is a direct extension of the Bell circuit:
- 1.Apply H to qubit 0 to create superposition: (|0⟩ + |1⟩)/√2 ⊗ |00⟩
- 2.Apply CNOT(0 → 1) to entangle qubit 1: (|00⟩ + |11⟩)/√2 ⊗ |0⟩
- 3.Apply CNOT(0 → 2) to entangle qubit 2: (|000⟩ + |111⟩)/√2
Each CNOT extends the entanglement by conditioning one more qubit on qubit 0. The pattern generalizes to n qubits with n-1 CNOT gates.
In a Bell state Φ+ = (|00⟩+|11⟩)/√2, measuring qubit 0 instantly fixes qubit 1. In GHZ, measuring qubit 0 instantly fixes both qubits 1 and 2. The correlations are three-way, not pairwise, no two-party entangled state between any pair of qubits can explain the joint statistics. This is what makes GHZ entanglement qualitatively different from stacking Bell pairs.
GHZ vs W States: Two Kinds of Multipartite Entanglement
Multipartite entanglement is not a single thing. The GHZ and W states represent two distinct classes of three-qubit entanglement that cannot be converted into each other by local operations:
GHZ = (|000⟩ + |111⟩)/√2, All-or-nothing correlation. Losing any one qubit (tracing it out) completely destroys all entanglement between the remaining two. The pair becomes fully separable. GHZ is fragile under qubit loss.
This is the opening of the lesson. The full walkthrough, the interactive circuit, and the graded challenge continue inside myqubit.
How this lesson works
A hands-on coding challenge. You write Qiskit-compatible Python in the browser editor, run it instantly via WebAssembly, watch the circuit and Bloch sphere react, and pass automatic output checks. The AI tutor Qubitus gives Socratic hints if you get stuck.
Part of: Entanglement & Protocols
Master multi-qubit systems, quantum teleportation, and cryptographic protocols.
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