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An Improved Semidefinite Programming Hierarchy for Testing Entanglement

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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 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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Authors and Affiliations

  1. MIT Center for Theoretical Physics, Cambridge, MA, USA

    Aram W. Harrow, Anand Natarajan & Xiaodi Wu

  2. Computer and Information Science Department, University of Oregon, Eugene, USA

    Xiaodi Wu

Authors
  1. Aram W. Harrow
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  2. Anand Natarajan
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  3. Xiaodi Wu
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Correspondence to Aram W. Harrow.

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Communicated by M. M. Wolf

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Harrow, A.W., Natarajan, A. & Wu, X. An Improved Semidefinite Programming Hierarchy for Testing Entanglement. Commun. Math. Phys. 352, 881–904 (2017). https://doi.org/10.1007/s00220-017-2859-0

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