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  • Semi-definite programming and quantum information

    This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations, providing a solid theoretical framework for addressing optimization challenges in quantum systems. By leveraging these tools, researchers and practitioners can characterize classical and quantum correlations,...

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  • Applications of semi-definite optimization in quantum information protocols

    Publication

    - Year 2016

    This work is concerned with the issue of applications of the semi-definite programming (SDP) in the field of quantum information sci- ence. Our results of the analysis of certain quantum information protocols using this optimization technique are presented, and an implementation of a relevant numerical tool is introduced. The key method used is NPA discovered by Navascues et al. [Phys. Rev. Lett. 98, 010401 (2007)]. In chapter...

  • Properties of dimension witnesses and their semidefinite programming relaxations

    Publication

    - PHYSICAL REVIEW A - Year 2014

    In this paper we develop a method for investigating semi-device-independent randomness expansion protocols that was introduced in Li et al. [H.-W. Li, P. Mironowicz, M. Pawłowski, Z.-Q. Yin, Y.-C. Wu, S. Wang, W. Chen, H.-G. Hu, G.-C. Guo, and Z.-F. Han, Phys. Rev. A 87, 020302(R) (2013)]. This method allows us to lower bound, with semi-definite programming, the randomness obtained from random number generators based on dimension...

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  • Connections between Mutually Unbiased Bases and Quantum Random Access Codes

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2018

    We present a new quantum communication complexity protocol, the promise--Quantum Random Access Code, which allows us to introduce a new measure of unbiasedness for bases of Hilbert spaces. The proposed measure possesses a clear operational meaning and can be used to investigate whether a specific number of mutually unbiased bases exist in a given dimension by employing Semi--Definite Programming techniques.

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  • Relationship between semi- and fully-device-independent protocols

    Publication
    • H. Li
    • P. A. Mironowicz
    • M. Pawłowski
    • Z. Yin
    • Y. Wu
    • S. Wang
    • W. Chen
    • H. Hu
    • G. Guo
    • Z. Han

    - PHYSICAL REVIEW A - Year 2013

    We study the relation between semi and fully device independent protocols. As a tool, we use the correspondence between Bell inequalities and dimension witnesses. We present a method for converting the former into the latter and vice versa. This relation provides us with interesting results for both scenarios. First, we find new random number generation protocols with higher bit rates for both the semi and fully device independent...

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