GHZ vs W States: Entanglement Robustness Under Particle Loss

Entangled State

Qubits in network N 4

Per-qubit loss probability p 30%

Live Readouts

|W₄⟩ = (|1000⟩+|0100⟩+|0010⟩+|0001⟩)/2

Qubits surviving

4 / 4

Pairwise concurrence C

0.500

N-party GHZ/W coherence

Intact

How it works

Two N-qubit states look similarly "maximally entangled" at first glance, but they belong to different entanglement classes (Dür, Vidal & Cirac, 2000) with opposite robustness:

|GHZ_N⟩ = (|00...0⟩ + |11...1⟩)/√2
|W_N⟩   = (1/√N) Σᵢ |0...1ᵢ...0⟩

Tracing out (losing) N−2 qubits and asking how entangled the two survivors still are gives a closed form for the pairwise concurrence C:

C(GHZ_N) = 0        for N ≥ 3   (1 only when N = 2)
C(W_N)   = 2 / N     for every N ≥ 2

GHZ's entanglement is entirely a global, all-or-nothing N-party correlation — reducing to any pair by tracing the rest destroys it completely, whether or not you actually "lose" a particle or just ignore it. W's entanglement is spread thin across every pair, so it survives losing up to N−2 of the N qubits, just growing weaker (∝ 1/N) rather than vanishing.

GHZ / W buttons — switch which N-qubit state the network holds.
N slider — number of qubits in the state; watch C(W_N) shrink as 2/N while C(GHZ_N) stays pinned at 0.
Loss probability slider + Trigger loss event — each qubit independently "goes missing" (photon absorbed, atom escapes the trap) with probability p; surviving qubits are redrawn with bonds sized by the real concurrence between them.
Reset — restores all N qubits before the next trial.

Real-world relevance: this is exactly why quantum-network engineers prefer W-class or graph/cluster states for multi-node entanglement distribution — a lost photon anywhere in a GHZ-based link kills all pairwise entanglement in the network, while a W-based link degrades gracefully.

Surviving qubit Lost qubit Entangled bond (brightness ∝ C)

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.