bibkey: han2026resistant authors: Zicheng Han; Wanchen Zhang; Xiande Zhang year: 2026 title: “A five-qubit 1-resistant graph state and stabilizer marginal certificates” doi: null url: https://arxiv.org/abs/2606.08561v1 claim: “The Discussion asks whether C5 and C6 are strongly m-resistant for m=1 and m=2 respectively.” strata_touched:

• D5/S3/Quantum/Entanglement/CycleSixStrongTwoResistanceRefutation license: citation-only triage: anchor

A five-qubit 1-resistant graph state and stabilizer marginal certificates

Page 8, Discussion:

Several open problems remain. First, do C₅ and C₆ give strongly m-resistant graph states for m = 1 and m = 2, respectively? Here, “strong” means genuine multipartite entanglement rather than mere entanglement.

The two clauses concern genuine multipartite entanglement after every loss of one and two qubits, respectively. The C₆ clause uses the strong-resistance definition of Zhang et al., arXiv:2505.06567. On zero-based labels, its amplitudes are (-1) raised to the sum of x_i x_(i+1 mod 6), divided by 8. The C₅ clause remains open here.

Page 2, Section II.A:

A mixed state ρ on H₁ ⊗ · · · ⊗ H_N is called fully separable if it can be written as

the displayed convex sum of products,

where p_α ≥ 0, ∑_α p_α = 1, and each ρ_i^(α) is a one-particle density operator

Page 2, Section II.B:

The graph state |G⟩ is obtained by preparing each qubit in

|+⟩ = (|0⟩ + |1⟩)/√2

and applying a controlled-Z gate along each edge:

|G⟩ = (∏_{{u,v} ∈ E} CZ_uv)|+⟩^⊗N.

Verified locator

• URL: https://arxiv.org/abs/2606.08561v1
• PDF: https://arxiv.org/pdf/2606.08561v1, page 8, Discussion; graph-state definition in Section II.B.