bibkey: quinta2019resistant authors: G. M. Quinta; R. André; A. Burchardt; K. Życzkowski year: 2019 title: “Cut-resistant links and multipartite entanglement resistant to particle loss” doi: 10.1103/PhysRevA.100.062329 url: https://arxiv.org/abs/1908.10390v1 claim: “For any N and m, there exists an m-resistant N-qudit state in some local dimension d.” strata_touched:
- D5/S3/Quantum/Entanglement/FullySeparableExchangeObstruction
- D5/S3/Quantum/Entanglement/MResistantQuditExistence license: citation-only triage: anchor
Verified locator
DOI: 10.1103/PhysRevA.100.062329
Publisher: https://doi.org/10.1103/PhysRevA.100.062329
Source: https://arxiv.org/abs/1908.10390v1
Definition
Section III, page 3:
Definition: (m-resistance) An entangled state of N parties is called m-resistant if:
- It remains entangled as any m of its N subsystems are traced away;
- It becomes separable if a partial trace is performed over an arbitrary set of m + 1 subsystems.
Conjecture
Section V, page 10:
Conjecture 1. For any N and m, there exists an m-resistant N-qudit state in some local dimension d.
The pure-state reading uses full separability as the separability predicate. The admissible range is N ≥ 3 and 0 ≤ m ≤ N − 2; a one-party marginal cannot be entangled. A qudit configuration is a function Fin N → Fin d, the pure density matrix has entries ψ(x) conjugate(ψ(y)), and normalization is the sum of the squared absolute values of the amplitudes. The same lost configuration is summed in the row and column of each partial trace.
Zhang et al., arXiv:2505.06567v1, Section II, page 2, equation (1):
A state is fully separable if it can be written as a convex combination of product states,
In finite local bases this is a finite convex sum of products of positive trace-one local matrices. Mixture weights are nonnegative real numbers whose sum is one. The local-basis type can be any finite type, including Fin d.
The later restatement and the previously known range m ≤ (N − 2)/2 are recorded in Zhang et al. and Han et al.. Ordinary entanglement here means failure of full separability; genuine multipartite entanglement is a stronger condition and is not the conjecture settled by this construction.