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A Practical Approach to SOS Relaxations for Detecting Quantum Entanglement

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  • Abhishek Bhardwaj

    (Australian National University)

Abstract

This article introduces PnCP, a MATLAB toolbox for constructing positive maps which are not completely positive. We survey optimization and sum of squares relaxation techniques to find the most numerically efficient methods and establish some benchmarks for this construction. We also show how this package can be applied to the problem of classifying entanglement in quantum states.

Suggested Citation

  • Abhishek Bhardwaj, 2023. "A Practical Approach to SOS Relaxations for Detecting Quantum Entanglement," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 869-891, September.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:3:d:10.1007_s10957-023-02258-5
    DOI: 10.1007/s10957-023-02258-5
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    References listed on IDEAS

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    1. Dik Bouwmeester & Jian-Wei Pan & Klaus Mattle & Manfred Eibl & Harald Weinfurter & Anton Zeilinger, 1997. "Experimental quantum teleportation," Nature, Nature, vol. 390(6660), pages 575-579, December.
    2. Igor Klep & Markus Schweighofer, 2013. "An Exact Duality Theory for Semidefinite Programming Based on Sums of Squares," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 569-590, August.
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