Qutrit witness from the Grothendieck constant of order four

Qutrit witness from the Grothendieck constant of order four In this paper, we prove that KG(3)<KG(4), where KG(d) denotes the Grothendieck constant of order d. To this end, we use a branch-and-bound algorithm commonly used in the solution of NP-hard problems. It has recently been proven that KG(3)≤1.4644. Here we prove that KG(4)≥1.4841, which has implications for device-independent witnessing dimensions greater than two. Furthermore, the algorithm with some modifications may find applications in various black-box quantum information tasks with large number of inputs and outputs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Qutrit witness from the Grothendieck constant of order four

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Qutrit witness from the Grothendieck constant of order four

Abstract

In this paper, we prove that KG(3)<KG(4), where KG(d) denotes the Grothendieck constant of order d. To this end, we use a branch-and-bound algorithm commonly used in the solution of NP-hard problems. It has recently been proven that KG(3)≤1.4644. Here we prove that KG(4)≥1.4841, which has implications for device-independent witnessing dimensions greater than two. Furthermore, the algorithm with some modifications may find applications in various black-box quantum information tasks with large number of inputs and outputs.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.012113
Publisher site
See Article on Publisher Site

Abstract

In this paper, we prove that KG(3)<KG(4), where KG(d) denotes the Grothendieck constant of order d. To this end, we use a branch-and-bound algorithm commonly used in the solution of NP-hard problems. It has recently been proven that KG(3)≤1.4644. Here we prove that KG(4)≥1.4841, which has implications for device-independent witnessing dimensions greater than two. Furthermore, the algorithm with some modifications may find applications in various black-box quantum information tasks with large number of inputs and outputs.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jul 13, 2017

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