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Article

Distance between Bound Entangled States from Unextendible Product Bases and Separable States

1
Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics, and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland
2
International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland
3
Institute of Informatics, Faculty of Mathematics, Physics, and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland
*
Author to whom correspondence should be addressed.
Quantum Rep. 2020, 2(1), 49-56; https://doi.org/10.3390/quantum2010004
Received: 30 November 2019 / Revised: 4 January 2020 / Accepted: 6 January 2020 / Published: 13 January 2020
We discuss the use of the Gilbert algorithm to tailor entanglement witnesses for unextendible product basis bound entangled states (UPB BE states). The method relies on the fact that an optimal entanglement witness is given by a plane perpendicular to a line between the reference state, entanglement of which is to be witnessed, and its closest separable state (CSS). The Gilbert algorithm finds an approximation of CSS. In this article, we investigate if this approximation can be good enough to yield a valid entanglement witness. We compare witnesses found with Gilbert algorithm and those given by Bandyopadhyay–Ghosh–Roychowdhury (BGR) construction. This comparison allows us to learn about the amount of entanglement and we find a relationship between it and a feature of the construction of UPBBE states, namely the size of their central tile. We show that in most studied cases, witnesses found with the Gilbert algorithm in this work are more optimal than ones obtained by Bandyopadhyay, Ghosh, and Roychowdhury. This result implies the increased tolerance to experimental imperfections in a realization of the state. View Full-Text
Keywords: bound entanglement; entanglement witness; Hilbert–Schmidt measure; optimization algorithms bound entanglement; entanglement witness; Hilbert–Schmidt measure; optimization algorithms
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MDPI and ACS Style

Wieśniak, M.; Pandya, P.; Sakarya, O.; Woloncewicz, B. Distance between Bound Entangled States from Unextendible Product Bases and Separable States. Quantum Rep. 2020, 2, 49-56. https://doi.org/10.3390/quantum2010004

AMA Style

Wieśniak M, Pandya P, Sakarya O, Woloncewicz B. Distance between Bound Entangled States from Unextendible Product Bases and Separable States. Quantum Reports. 2020; 2(1):49-56. https://doi.org/10.3390/quantum2010004

Chicago/Turabian Style

Wieśniak, Marcin, Palash Pandya, Omer Sakarya, and Bianka Woloncewicz. 2020. "Distance between Bound Entangled States from Unextendible Product Bases and Separable States" Quantum Reports 2, no. 1: 49-56. https://doi.org/10.3390/quantum2010004

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