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_ABI (ρ^TA_ABI) increases with F but decreases with the variable y, while the variation of the negativity N_BIBII(ρ^TA_ABI) is opposite to that of the negativity N_ABI (ρ^TA_ABI). We also study the von Neumann entropies S(ρ_ABI) and S(ρ_BIBII). We find that the S(ρ_ABI) increases with variable y but S(ρ_BIBII) is independent of it. However, both S(ρ_ABI) and S(ρ_BIBII) first decreases with F and then increases with it. The concurrences C(ρ_ABI) and C(ρ_BIBII) 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.

Keywords

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

References

[1] P. M. Alsing and G. J. Milburn, Teleportation with a uniformly accelerated partner, Phys. Rev. Lett. 91(18), 180404 (2003)

[2] A. Peres and D. R. Terno, Quantum information and relativity theory, Rev. Mod. Phys. 76(1), 93 (2004) (and references therein)

[3] I. Fuentes-Schuller and R. B. Mann, Alice falls into a black hole: Entanglement in noninertial frames, Phys. Rev. Lett. 95(12), 120404 (2005)

[4] L. Lamata, M. A. Martin-Delgado, and E. Solano, Relativity and Lorentz invariance of entanglement distillability, Phys. Rev. Lett. 97(25), 250502 (2006)

[5] 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)

[6] K. Bradler, Eavesdropping of quantum communication from a noninertial frame, Phys. Rev. A 75(2), 022311 (2007)

[7] Y. C. Ou and H. Fan, Monogamy inequality in terms of negativity for three-qubit states, Phys. Rev. A 75(6), 062308 (2007)

[8] 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)

[9] J. Wang and J. Jing, Multipartite entanglement of fermionic systems in noninertial frames, Phys. Rev. A 83(2), 022314 (2011)

[10] M.-R. Hwang, D. Park, and E. Jung, Tripartite entanglement in noninertial frame, Phys. Rev. A 83, 012111 (2001)

[11] 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)

[12] S. Khan, Tripartite entanglement of fermionic system in accelerated frames, Ann. Phys. 348, 270 (2014)

[13] 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)

[14] 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)

[15] E. Martín-Martínez and I. Fuentes, Redistribution of particle and antiparticle entanglement in noninertial frames, Phys. Rev. A 83(5), 052306 (2011)

[16] I. Fuentes-Schuller and R. B. Mann, Alice falls into a black hole: Entanglement in noninertial frames, Phys. Rev. Lett. 95(12), 120404 (2005)

[17] 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)

[18] 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)

[19] S. Moradi, Distillability of entanglement in accelerated frames, Phys. Rev. A 79(6), 064301 (2009)

[20] H. Mehri-Dehnavi, B. Mirza, H. Mohammadzadeh, and R. Rahimi, Pseudo-entanglement evaluated in noninertial frames, Ann. Phys. 326(5), 1320 (2011)

[21] R. F. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys. Rev. A 40(8), 4277 (1989)

[22] W. C. Qiang, Q. Dong, G. H. Sun and S. H. Dong (submitted)

[23] R. A. Horn and C. R. Johnson, Matrix Analysis, New York: Cambridge University Press, 1985, pp 205–415, 441

[24] 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)

[25] S. A. Najafizade, H. Hassanabadi, and S. Zarrinkamar, Nonrelativistic Shannon information entropy for Kratzer potential, Chin. Phys. B 25(4), 040301 (2016)

[26] S. A. Najafizade, H. Hassanabadi, and S. Zarrinkamar, Nonrelativistic Shannon information entropy for Killingbeck potential, Can. J. Phys. 94(10), 1085 (2016)

[27] Y. Q. Li and G. Q. Zhu, Concurrence vectors for entanglement of high-dimensional systems, Front. Phys. China 3(3), 250 (2008)

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