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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. M. Alsing and G. J. Milburn, Teleportation with a uniformly accelerated partner, Phys. Rev. Lett. 91(18), 180404 (2003)
A. Peres and D. R. Terno, Quantum information and relativity theory, Rev. Mod. Phys. 76(1), 93 (2004) (and references therein)
I. Fuentes-Schuller and R. B. Mann, Alice falls into a black hole: Entanglement in noninertial frames, Phys. Rev. Lett. 95(12), 120404 (2005)
L. Lamata, M. A. Martin-Delgado, and E. Solano, Relativity and Lorentz invariance of entanglement distillability, Phys. Rev. Lett. 97(25), 250502 (2006)
P. M. Alsing, I. Fuentes-Schuller, R. B. Mann, and T. E. Tessier, Entanglement of Dirac fields in noninertial frames, Phys. Rev. A 74(3), 032326 (2006)
K. Bradler, Eavesdropping of quantum communication from a noninertial frame, Phys. Rev. A 75(2), 022311 (2007)
Y. C. Ou and H. Fan, Monogamy inequality in terms of negativity for three-qubit states, Phys. Rev. A 75(6), 062308 (2007)
D. E. Bruschi, J. Louko, E. Martín-Martínez, A. Dragan, and I. Fuentes, Unruh effect in quantum information beyond the single-mode approximation, Phys. Rev. A 82(4), 042332 (2008)
J. Wang and J. Jing, Multipartite entanglement of fermionic systems in noninertial frames, Phys. Rev. A 83(2), 022314 (2011)
M.-R. Hwang, D. Park, and E. Jung, Tripartite entanglement in noninertial frame, Phys. Rev. A 83, 012111 (2001)
Y. Yao, X. Xiao, L. Ge, X. G. Wang, and C. P. Sun, Quantum Fisher information in noninertial frames, Phys. Rev. A 89(4), 042336 (2014)
S. Khan, Tripartite entanglement of fermionic system in accelerated frames, Ann. Phys. 348, 270 (2014)
S. Khan, N. A. Khan, and M. K. Khan, Non-maximal tripartite entanglement degradation of Dirac and scalar fields in non-inertial frames, Commum. Theor. Phys. 61(3), 281 (2014)
D. E. Bruschi, A. Dragan, I. Fuentes, and J. Louko, Particle and antiparticle bosonic entanglement in noninertial frames, Phys. Rev. D 86(2), 025026 (2012)
E. Martín-Martínez and I. Fuentes, Redistribution of particle and antiparticle entanglement in noninertial frames, Phys. Rev. A 83(5), 052306 (2011)
I. Fuentes-Schuller and R. B. Mann, Alice falls into a black hole: Entanglement in noninertial frames, Phys. Rev. Lett. 95(12), 120404 (2005)
X. Xiao, Y. M. Xie, Y. Yao, Y. L. Li, and J. Wang, Retrieving the lost fermionic entanglement by partial measurement in noninertial frames, Ann. Phys. 390, 83 (2018)
W. C. Qiang, G. H. Sun, O. Camacho-Nieto, and S. H. Dong, Multipartite entanglement of fermionic systems in noninertial frames revisited, arXiv: 1711.04230 (2017)
S. Moradi, Distillability of entanglement in accelerated frames, Phys. Rev. A 79(6), 064301 (2009)
H. Mehri-Dehnavi, B. Mirza, H. Mohammadzadeh, and R. Rahimi, Pseudo-entanglement evaluated in noninertial frames, Ann. Phys. 326(5), 1320 (2011)
R. F. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys. Rev. A 40(8), 4277 (1989)
W. C. Qiang, Q. Dong, G. H. Sun and S. H. Dong (submitted)
R. A. Horn and C. R. Johnson, Matrix Analysis, New York: Cambridge University Press, 1985, pp 205, 415, 441
W. C. Qiang, G. H. Sun, Q. Dong, and S. H. Dong, Genuine multipartite concurrence for entanglement of Dirac fields in noninertial frames, Phys. Rev. A 98(2), 022320 (2018)
S. A. Najafizade, H. Hassanabadi, and S. Zarrinkamar, Nonrelativistic Shannon information entropy for Kratzer potential, Chin. Phys. B 25(4), 040301 (2016)
S. A. Najafizade, H. Hassanabadi, and S. Zarrinkamar, Nonrelativistic Shannon information entropy for Killingbeck potential, Can. J. Phys. 94(10), 1085 (2016)
Y. Q. Li and G. Q. Zhu, Concurrence vectors for entanglement of high-dimensional systems, Front. Phys. China 3(3), 250 (2008)
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dong, Q., Torres-Arenas, A.J., Sun, GH. 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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11467-018-0876-x