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Entanglement Sudden Death in Gapped Ground States

  • Robert Ferydouni
  • Thomas Jackson
  • Samuel O. Scalet
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Abstract

Spatial sudden death of entanglement refers to the disappearance of quantum correlations between subsystems after a certain distance called the entanglement length. Specifically, given a density matrix ρABC on a tripartite system ABC with B spatially separating A and C, the entanglement length is the distance ℓ(A,C) after which the reduced density matrix ρAC, given by tracing out the B subsystem, is separable. We show in the case of gapped ground states in any dimension that the entanglement length is finite on finite subsystems. Restricting to one-dimensional systems, we prove that normal matrix product states have a finite entanglement length independent of A and C, and that a finite pure state with such uniform entanglement length has a matrix product state representation with bond dimension independent of A and C. Consequently, in one dimension, entanglement length distinguishes matrix product states from all other pure states.

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Cite

BibTeXRIS
BibTeX
@misc{ferydouni2026entanglement,
  title = {{Entanglement Sudden Death in Gapped Ground States}},
  author = {Robert Ferydouni and Thomas Jackson and Samuel O. Scalet},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17038},
  eprint = {2610.17038},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17038},
}
RIS
TY  - UNPB
TI  - Entanglement Sudden Death in Gapped Ground States
AU  - Robert Ferydouni
AU  - Thomas Jackson
AU  - Samuel O. Scalet
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17038
UR  - https://arxiv.org/abs/2610.17038
AB  - Spatial sudden death of entanglement refers to the disappearance of quantum correlations between subsystems after a certain distance called the entanglement length. Specifically, given a density matrix ρ_ABC on a tripartite system ABC with B spatially separating A and C, the entanglement length is the distance ℓ(A,C) after which the reduced density matrix ρ_AC, given by tracing out the B subsystem, is separable. We show in the case of gapped ground states in any dimension that the entanglement length is finite on finite subsystems. Restricting to one-dimensional systems, we prove that normal matrix product states have a finite entanglement length independent of A and C, and that a finite pure state with such uniform entanglement length has a matrix product state representation with bond dimension independent of A and C. Consequently, in one dimension, entanglement length distinguishes matrix product states from all other pure states.
ER  -