Communications in Mathematical Physics

, Volume 352, Issue 3, pp 881–904 | Cite as

An Improved Semidefinite Programming Hierarchy for Testing Entanglement

  • Aram W. HarrowEmail author
  • Anand Natarajan
  • Xiaodi Wu


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 that 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.


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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.MIT Center for Theoretical PhysicsCambridgeUSA
  2. 2.Computer and Information Science DepartmentUniversity of OregonEugeneUSA

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