bibkey: zhang2025resistant authors: Wanchen Zhang; Zicheng Han; Fei Shi; Xiande Zhang year: 2025 title: “New constructions of multipartite entanglement resistant to particle loss” doi: null url: https://arxiv.org/abs/2505.06567v1 claim: “Definition 2 requires initial GME, GME after every m-particle loss, and full separability after every (m+1)-particle loss.” strata_touched:
- D5/S3/Quantum/Entanglement/CycleSixStrongTwoResistanceRefutation license: citation-only triage: anchor
New constructions of multipartite entanglement resistant to particle loss
Page 3, Definition 2:
A genuinely entangled state |ϕ⟩ is called strong m-resistant if it satisfies the following properties:
- ρ_J̄(ϕ) is genuinely entangled for any J ⊂ [N] with |J| = m.
- ρ_J̄(ϕ) is fully separable for any J ⊂ [N] with |J| = m + 1.
Page 2, following equation (3):
where the first sum goes over all bipartitions of [N]. If a state does admit such a decomposition, it is called biseparable
Page 2, preceding equation (3):
An N-particle state ρ on Hilbert space H₁ ⊗ · · · ⊗ H_N is genuinely entangled if it cannot be decomposed into as
Page 2, preceding equations (1) and (2):
A state is fully separable if it can be written as a convex combination of product states,
Take the partial trace over all particles in J ⊂ [N], and denote the reduced state
ρ_J̄(ψ) ≜ Tr_J(|ψ⟩⟨ψ|).
Equation (3) is the convex sum over bipartitions of convex mixtures of products of density matrices on the two factors. Equivalently, flatten both finite mixtures into one finite convex sum, permitting a different nontrivial cut in each term. GME is the negation of this predicate. Full separability is a finite convex combination of products of individual single-qubit density matrices. Equation (2) defines the loss marginal as Tr_J(|ψ⟩⟨ψ|).
Verified locator
- URL: https://arxiv.org/abs/2505.06567v1
- PDF: https://arxiv.org/pdf/2505.06567v1, Section II, equations (2) and (3), and Definition 2 on page 3.