English

An improved semidefinite programming hierarchy for testing entanglement

Quantum Physics 2017-06-19 v2 Data Structures and Algorithms Optimization and Control

Abstract

We present a stronger version of the Doherty-Parrilo-Spedalieri (DPS) hierarchy of approximations for the set of separable states. Unlike DPS, our hierarchy converges exactly at a finite number of rounds for any fixed input dimension. This yields an algorithm for separability testing which is singly exponential in dimension and polylogarithmic in accuracy. Our analysis makes use of tools from algebraic geometry, but our algorithm is elementary and differs from DPS only by one simple additional collection of constraints.

Keywords

Cite

@article{arxiv.1506.08834,
  title  = {An improved semidefinite programming hierarchy for testing entanglement},
  author = {Aram W. Harrow and Anand Natarajan and Xiaodi Wu},
  journal= {arXiv preprint arXiv:1506.08834},
  year   = {2017}
}

Comments

22 pages. v2: published version, adds numerical results. Matlab code available at https://github.com/isobovine/dpsplus/

R2 v1 2026-06-22T10:02:33.277Z