IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v180y2019i3d10.1007_s10957-018-1357-7.html
   My bibliography  Save this article

Calculating Entanglement Eigenvalues for Nonsymmetric Quantum Pure States Based on the Jacobian Semidefinite Programming Relaxation Method

Author

Listed:
  • Mengshi Zhang

    (National University of Defense Technology)

  • Xinzhen Zhang

    (Tianjin University)

  • Guyan Ni

    (National University of Defense Technology)

Abstract

The geometric measure of entanglement is a widely used entanglement measure for quantum pure states. The key problem of computation of the geometric measure is to calculate the entanglement eigenvalue, which is equivalent to computing the largest unitary eigenvalue of a corresponding complex tensor. In this paper, we propose a Jacobian semidefinite programming relaxation method to calculate the largest unitary eigenvalue of a complex tensor. For this, we first introduce the Jacobian semidefinite programming relaxation method for a polynomial optimization with equality constraint and then convert the problem of computing the largest unitary eigenvalue to a real equality constrained polynomial optimization problem, which can be solved by the Jacobian semidefinite programming relaxation method. Numerical examples are presented to show the availability of this approach.

Suggested Citation

  • Mengshi Zhang & Xinzhen Zhang & Guyan Ni, 2019. "Calculating Entanglement Eigenvalues for Nonsymmetric Quantum Pure States Based on the Jacobian Semidefinite Programming Relaxation Method," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 787-802, March.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1357-7
    DOI: 10.1007/s10957-018-1357-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1357-7
    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/s10957-018-1357-7?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. Guyan Ni & Minru Bai, 2016. "Spherical optimization with complex variablesfor computing US-eigenpairs," Computational Optimization and Applications, Springer, vol. 65(3), pages 799-820, December.
    2. Gaohang Yu & Zefeng Yu & Yi Xu & Yisheng Song & Yi Zhou, 2016. "An adaptive gradient method for computing generalized tensor eigenpairs," Computational Optimization and Applications, Springer, vol. 65(3), pages 781-797, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mengshi Zhang & Guyan Ni & Guofeng Zhang, 2020. "Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement," Computational Optimization and Applications, Springer, vol. 75(3), pages 779-798, April.

    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. Mengshi Zhang & Guyan Ni & Guofeng Zhang, 2020. "Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement," Computational Optimization and Applications, Springer, vol. 75(3), pages 779-798, April.
    2. Na Zhao & Qingzhi Yang & Yajun Liu, 2017. "Computing the generalized eigenvalues of weakly symmetric tensors," Computational Optimization and Applications, Springer, vol. 66(2), pages 285-307, March.

    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:180:y:2019:i:3:d:10.1007_s10957-018-1357-7. 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.