IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v198y2023i3d10.1007_s10957-023-02258-5.html
   My bibliography  Save this article

A Practical Approach to SOS Relaxations for Detecting Quantum Entanglement

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02258-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-023-02258-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:arp:sjossm:2021:p:93-99 is not listed on IDEAS
    2. Karthik, Mekala & Lalwani, Jitesh & Jajodia, Babita, 2022. "Proposed Quantum Text Teleportation Protocol (QTTP) for Secure Text Transfer by using Quantum Teleportation and Huffman Coding," OSF Preprints 4svxf, Center for Open Science.
    3. Wenyuan Liu & Andrea Nanetti & Siew Ann Cheong, 2017. "Knowledge evolution in physics research: An analysis of bibliographic coupling networks," PLOS ONE, Public Library of Science, vol. 12(9), pages 1-19, September.
    4. Liang Xiang & Jiachen Chen & Zitian Zhu & Zixuan Song & Zehang Bao & Xuhao Zhu & Feitong Jin & Ke Wang & Shibo Xu & Yiren Zou & Hekang Li & Zhen Wang & Chao Song & Alexander Yue & Justine Partridge & , 2024. "Enhanced quantum state transfer by circumventing quantum chaotic behavior," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    5. Sebastian Philipp Neumann & Alexander Buchner & Lukas Bulla & Martin Bohmann & Rupert Ursin, 2022. "Continuous entanglement distribution over a transnational 248 km fiber link," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    6. María López Quijorna, 2021. "Detecting optimality and extracting solutions in polynomial optimization with the truncated GNS construction," Journal of Global Optimization, Springer, vol. 81(3), pages 559-598, November.
    7. Abouelkhir, N. & EL Hadfi, H. & Slaoui, A. & Ahl Laamara, R., 2023. "A simple analytical expression of quantum Fisher and Skew information and their dynamics under decoherence channels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 612(C).
    8. Dario Lago-Rivera & Jelena V. Rakonjac & Samuele Grandi & Hugues de Riedmatten, 2023. "Long distance multiplexed quantum teleportation from a telecom photon to a solid-state qubit," Nature Communications, Nature, vol. 14(1), pages 1-6, December.
    9. Seida, C. & Seddik, S. & Hassouni, Y. & Allati, A. El, 2022. "Memory effects on bidirectional teleportation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    10. Haonan Wang & Heejun Kim & Duanfei Dong & Keisuke Shinokita & Kenji Watanabe & Takashi Taniguchi & Kazunari Matsuda, 2024. "Quantum coherence and interference of a single moiré exciton in nano-fabricated twisted monolayer semiconductor heterobilayers," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    11. Kai Kellner & Marc E. Pfetsch & Thorsten Theobald, 2019. "Irreducible Infeasible Subsystems of Semidefinite Systems," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 727-742, June.
    12. Xiaodong Qiu & Haoxu Guo & Lixiang Chen, 2023. "Remote transport of high-dimensional orbital angular momentum states and ghost images via spatial-mode-engineered frequency conversion," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    13. Peter J. Olver, 2022. "Motion and Continuity," The Mathematical Intelligencer, Springer, vol. 44(3), pages 241-249, September.
    14. Leilei Li & Hengji Li & Chaoyang Li & Xiubo Chen & Yan Chang & Yuguang Yang & Jian Li, 2018. "The security analysis of E91 protocol in collective-rotation noise channel," International Journal of Distributed Sensor Networks, , vol. 14(5), pages 15501477187, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:198:y:2023:i:3:d:10.1007_s10957-023-02258-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.