An improved semidefinite programming hierarchy for testing entanglement

June 29, 2015 · Entered Twilight · 🏛 Communications in Mathematical Physics

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Authors Aram W. Harrow, Anand Natarajan, Xiaodi Wu arXiv ID 1506.08834 Category quant-ph: Quantum Computing Cross-listed cs.DS, math.OC Citations 36 Venue Communications in Mathematical Physics Repository https://github.com/isobovine/dpsplus/ ⭐ 1 Last Checked 1 month ago

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.