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Maximally entangled states in discrete and Gaussian regimes

  • Youngrong Lim
  • Jaewan Kim
  • Soojoon Lee
  • Kabgyun Jeong
Article

Abstract

We study a relation between discrete-variable quantum states and continuous-variable (especially, restricted on Gaussian) ones. In the previous work, we have investigated an information-theoretic correspondence between the Gaussian maximally mixed states and their purifications as Gaussian maximally entangled states in Jeong and Lim (Phys Lett A 380:3607, 2016). We here compare the purified continuous-variable maximally entangled state with a two-mode squeezed vacuum state, which is a conventional entangled state in Gaussian regime, by the explicit calculation of quantum fidelities between those states and an \(N\times N\)-dimensional maximally entangled state in the finite Hilbert space. Consequently, we naturally conclude that the purified maximally entangled state is more suitable to the Gaussian maximally entangled state than the two-mode squeezed vacuum state, in a sense that it might be useful for continuous-variable quantum information tasks in which entangled states are needed.

Keywords

Gaussian maximally entangled (mixed)state Two-mode squeezed vacuum state Dimension-mode matching Qutrit Bell test Photon number entangled state 

Notes

Acknowledgements

This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1A6A3A01007264) and the Ministry of Science and ICT (NRF-2016R1A2B4014928). J.K. appreciates the financial support by the KIST Institutional Program (Project No. 2E26680-16-P025). K.J. acknowledges financial support by the National Research Foundation of Korea (NRF) through a grant funded by the Ministry of Science and ICT (NRF-2017R1E1A1A03070510 and NRF-2017R1A5A1015626) and the Ministry of Education (NRF-2018R1D1A1B07047512).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Research Institute for Basic SciencesKyung Hee UniversitySeoulKorea
  2. 2.IMDARC, Department of Mathematical SciencesSeoul National UniversitySeoulKorea
  3. 3.School of Computational SciencesKorea Institute for Advanced StudySeoulKorea

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