Entanglement transitivity problems

Gelo Noel M. Tabia, Kai Siang Chen, Chung Yun Hsieh, Yu Chun Yin, Yeong Cherng Liang

Research output: Contribution to journalArticlepeer-review


One of the goals of science is to understand the relation between a whole and its parts, as exemplified by the problem of certifying the entanglement of a system from the knowledge of its reduced states. Here, we focus on a different but related question: can a collection of marginal information reveal new marginal information? We answer this affirmatively and show that (non-) entangled marginal states may exhibit (meta)transitivity of entanglement, i.e., implying that a different target marginal must be entangled. By showing that the global n-qubit state compatible with certain two-qubit marginals in a tree form is unique, we prove that transitivity exists for a system involving an arbitrarily large number of qubits. We also completely characterize—in the sense of providing both the necessary and sufficient conditions—when (meta)transitivity can occur in a tripartite scenario when the two-qudit marginals given are either the Werner states or the isotropic states. Our numerical results suggest that in the tripartite scenario, entanglement transitivity is generic among the marginals derived from pure states.

Original languageEnglish
Article number98
Journalnpj Quantum Information
Issue number1
Publication statusPublished - 2022 Dec

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Statistical and Nonlinear Physics
  • Computer Networks and Communications
  • Computational Theory and Mathematics


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