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Research · Bell State · Fidelity Decomposition

The Collapse of Multipartite Entanglement: A First-Person Benchmark of GHZ State Fidelity

Raja Ram · Kryptur OU · Tallinn, Estonia
GHZ Entanglement Research 2026 · Published June 8, 2026

10.5281/zenodo.20600777

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Fidelity vs. qubit count

GHZ state fidelity versus qubit number N

Peak fidelity

0.9307

4-qubit GHZ · ibm_marrakesh

Collapse point

Qubits where parity signal extinguishes

Minimum F

0.0453

80-qubit state ≈ maximally mixed

Shots

8,192

Per circuit · Z and X basis

Abstract

I report a hands-on, systematic investigation of Greenberger–Horne–Zeilinger (GHZ) state generation on a 127-qubit superconducting quantum processor, covering system sizes from 4 to 80 qubits. I measured both computational-basis populations and global Pauli-X parity oscillations to decompose fidelity into population purity and phase-coherence components. A 4-qubit GHZ state achieves F = 0.9307, yet by 32 qubits fidelity plummets to 0.0963; at 80 qubits the state is indistinguishable from maximally mixed (F = 0.0453).

Introduction

The Greenberger–Horne–Zeilinger (GHZ) state is the ultimate test of a quantum processor's ability to sustain global superposition. Its fidelity is exquisitely sensitive to noise—a single qubit error can collapse the entire entangled edifice.

|GHZ_N⟩ = (1/√2)(|0⟩^⊗N + |1⟩^⊗N)

Entanglement fuels quantum key distribution, quantum-enhanced metrology, and measurement-based computation. I set out to map the true usability frontier for a cloud-accessible 127-qubit processor.

Theoretical Framework

Fidelity Decomposition

For an ideal GHZ state, P_Z = 1 and ⟨X^⊗N⟩ = 1. The fidelity estimator is:

F = ½(P_Z + ⟨X^⊗N⟩)

Exponential Sensitivity

Each qubit adds CNOT gate error (ε_cx ≈ 0.5–1%) and depth-driven dephasing. Fidelity drops as F(N) ≈ exp(−αN).

Experimental Design

Experiments on IBM Quantum ibm_marrakesh (127 qubits, heavy-hex topology). For N ∈ {4, 32, 64, 80} I built Z-basis and X-basis circuits, transpiled at level 3, 8192 shots each via Qiskit Runtime Sampler.

Z-basis circuit — **Figure 1.** GHZ preparation and measurement circuits (N=4). X-basis variant adds Hadamard gates before readout.

Results and Analysis

Fidelity Collapse

Table 1. Measured GHZ fidelity on ibm_marrakesh (8192 shots)

N	F	P_Z	⟨X^⊗N⟩
4	0.9307	0.9583	0.9031
32	0.0963	0.2902	−0.0977
64	0.1097	0.2092	0.0103
80	0.0453	0.1045	−0.0139

GHZ fidelity vs qubit number — **Figure 2.** Fidelity vs. N. Hardware fidelities decay exponentially (α ≈ 0.07–0.08).

Entanglement Breakdown

**Figure 3.** Measurement histograms for the 4-qubit GHZ state. Top row: Z basis; bottom row: X basis. Left: ideal simulation; right: ibm_marrakesh hardware.

Noise Channels

CNOT gate errors

ε_cx ~ 0.5–1% per gate; N−1 CNOT chain accumulates error exponentially.

Dephasing

Depth scales with N; qubits exposed to T₂ ~ 80–150 μs.

Readout errors

1–3% assignment error contaminates Z-basis population purity.

Crosstalk & ZZ coupling

Stray interactions on the 127-qubit chip corrupt the GHZ chain.

Comparative Benchmarks

Table 2. GHZ benchmarks across platforms

Qubits	Fidelity	Noise limits	Mitigation
32 (this work)	0.0963	Dephasing, crosstalk	None
80 (this work)	0.0453	Dephasing scaling	None
120 (mitigated)	0.56	Residual coherent errors	Adaptive comp., DD
56 (trapped-ion)	0.6156	Gate scaling	Logarithmic fanout

Conclusion

4-qubit entanglement is robust (F = 0.9307), but fidelity decays exponentially to 0.0453 at 80 qubits. Phase coherence extinguishes beyond 32 qubits. These results define the usability frontier for raw multipartite entanglement and underscore the role of error mitigation.

Full paper, data & circuits

DOI 10.5281/zenodo.20600777 · Open access · CC BY 4.0

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