Entanglement measures of a new type pseudo-pure state in accelerated frames

Abstract

In this work we analyze the characteristics of quantum entanglement of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will help us to understand the relationship between the relativity and quantum information theory. Some states will be changed from entangled states into separable ones around the critical value F = 1/4, but there is no such a critical value for the variable y related to acceleration a. We find that the negativity \({N_{A{B_I}}}\left( {\rho _{A{B_I}}^{{T_A}}} \right)\) increases with F but decreases with the variable y, while the variation of the negativity \({N_{{B_I}{B_{II}}}}\left( {\rho _{{B_I}{B_{II}}}^{{T_{{B_I}}}}} \right)\) is opposite to that of the negativity \({N_{A{B_I}}}\left( {\rho _{A{B_I}}^{{T_A}}} \right)\). We also study the von Neumann entropies S(ρABI) and S(ρBIBII). We find that the S(ρABI) increases with variable y but S(ρBIBII ) is independent of it. However, both S(ρABI) and S(ρBIBII ) first decreases with F and then increases with it. The concurrences C(ρABI) and C(ρBIBII) are also discussed. We find that the former decreases with y while the latter increases with y but both of them first increase with F and then decrease with it.

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Acknowledgements

We would like to thank the kind referees for invaluable and positive suggestions, which have improved the manuscript greatly. This work was supported by project 20180677- SIP-IPN, COFAA-IPN, Mexico and partially by the CONACYT project under Grant No. 288856-CB-2016.

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Correspondence to Qian Dong.

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Dong, Q., Torres-Arenas, A.J., Sun, G. et al. Entanglement measures of a new type pseudo-pure state in accelerated frames. Front. Phys. 14, 21603 (2019). https://doi.org/10.1007/s11467-018-0876-x

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Keywords

  • negativity
  • pseudo-pure state
  • noninertial frame
  • entanglement
  • von Neumann entropy
  • concurrence