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.
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/