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An Improved Semidefinite Programming Hierarchy for Testing Entanglement
Name
1506.08834.pdf
Description
Accepted version
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764.06 KB
Format
Adobe PDF
Checksum (MD5)
94da428ea38226fe4ce7bca03408eed2
Author(s)
Harrow, Aram W
Natarajan, Anand
Wu, Xiaodi
Date Issued
2017
Journal
Communications in Mathematical Physics
Publisher
Springer Nature
Citation
Harrow, A. W., A. Natarajan, and X. Wu. "An Improved Semidefinite Programming Hierarchy for Testing Entanglement." Communications in Mathematical Physics 352 3 (2017): 881-904.
Version
Author's final manuscript
Abstract
© 2017, Springer-Verlag Berlin Heidelberg. 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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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
10.1007/S00220-017-2859-0
