Abstract
We study the quantum coherence in de Sitter space for the bipartite system of Alice and Bob who initially share an entangled state between the two modes of a free massive scalar field. It is shown that the space-curvature effect can produce both local coherence and correlated coherence, leading to the increase of the total coherence of the bipartite system. These results are sharp different from the Unruh effect or Hawking effect, which, in the single mode approximation, cannot produce local coherence and at the same time destroy correlated coherence, leading to the decrease of the total coherence of the bipartite systems. Interestingly, we find that quantum coherence has the opposite behavior compared with the quantum correlation in de Sitter space. We also find that quantum coherence is most severely affected by the curvature effect of de Sitter space for the cases of conformal invariance and masslessness. Our result reveals the difference between the curvature effect in the de Sitter space and the Unruh effect in Rindler spacetime or the Hawking effect in black hole spacetime on quantum coherence.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.J. Leggett, Macroscopic quantum systems and the quantum theory of measurement, Prog. Theor. Phys. Suppl. 69 (2013) 80.
M.A. Nielsen and I.L. Chuang, Quantum computation and quantum information, 10th edition, Cambridge University Press, Cambridge, U.K. (2010).
A. Streltsov, G. Adesso and M.B. Plenio, Quantum coherence as a resource, Rev. Mod. Phys. 89 (2017) 041003 [arXiv:1609.02439] [INSPIRE].
R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81 (2009) 865 [quant-ph/0702225] [INSPIRE].
A. Einstein, B. Podolsky and N. Rosen, Can quantum mechanical description of physical reality be considered complete?, Phys. Rev. 47 (1935) 777 [INSPIRE].
K.C. Tan, H. Kwon, C.-Y. Park and H. Jeong, Unified view of quantum correlations and quantum coherence, Phys. Rev. A 94 (2016) 022329 [Erratum ibid. 96 (2017) 069905].
Y. Guo and S. Goswami, Discordlike correlation of bipartite coherence, Phys. Rev. A 95 (2017) 062340.
B. Schumacher and M.D. Westmoreland, Quantum privacy and quantum coherence, Phys. Rev. Lett. 80 (1998) 5695 [quant-ph/9709058] [INSPIRE].
S.E. Barnes, R. Ballou, B. Barbara and J. Strelen, Quantum coherence in small antiferromagnets, Phys. Rev. Lett. 79 (1997) 289.
U.K. Sharma, I. Chakrabarty and M.K. Shukla, Broadcasting quantum coherence via cloning, Phys. Rev. A 96 (2017) 052319.
Y. Peng, Y. Jiang and H. Fan, Maximally coherent states and coherence-preserving operations, Phys. Rev. A 93 (2016) 032326.
F. Brandão, M. Horodecki, N. Ng, J. Oppenheim and S. Wehner, The second laws of quantum thermodynamics, Proc. Nat. Acad. Sci. 112 (2015) 3275.
M. Horodecki and J. Oppenheim, Fundamental limitations for quantum and nanoscale thermodynamics, Nature Commun. 4 (2013) 2059.
P. Ćwikliński, M. Studziński, M. Horodecki and J. Oppenheim, Limitations on the evolution of quantum coherences: towards fully quantum second laws of thermodynamics, Phys. Rev. Lett. 115 (2015) 210403.
S.F. Huelga and M.B. Plenio, A vibrant environment, Nature Phys. 10 (2014) 621.
S. Huelga and M. Plenio, Vibrations, quanta and biology, Contemp. Phys. 54 (2013) 181.
M. Gärttner, P. Hauke and A.M. Rey, Relating out-of-time-order correlations to entanglement via multiple-quantum coherences, Phys. Rev. Lett. 120 (2018) 040402 [arXiv:1706.01616] [INSPIRE].
T. Baumgratz, M. Cramer and M. Plenio, Quantifying coherence, Phys. Rev. Lett. 113 (2014) 140401.
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
S.W. Hawking, Black hole explosions?, Nature 248 (1974) 30.
J.L. Ball, I. Fuentes-Schuller and F.P. Schuller, Entanglement in an expanding spacetime, Phys. Lett. A 359 (2006) 550 [quant-ph/0506113] [INSPIRE].
Y. Nambu and Y. Ohsumi, Classical and quantum correlations of scalar field in the inflationary universe, Phys. Rev. D 84 (2011) 044028 [arXiv:1105.5212] [INSPIRE].
S. Kanno, J. Murugan, J.P. Shock and J. Soda, Entanglement entropy of α-vacua in de Sitter space, JHEP 07 (2014) 072 [arXiv:1404.6815] [INSPIRE].
I. Fuentes-Schuller and R.B. Mann, Alice falls into a black hole: entanglement in non-inertial frames, Phys. Rev. Lett. 95 (2005) 120404 [quant-ph/0410172] [INSPIRE].
P.M. Alsing, I. Fuentes-Schuller, R.B. Mann and T.E. Tessier, Entanglement of Dirac fields in non-inertial frames, Phys. Rev. A 74 (2006) 032326 [quant-ph/0603269] [INSPIRE].
G. Adesso, I. Fuentes-Schuller and M. Ericsson, Continuous variable entanglement sharing in non-inertial frames, Phys. Rev. A 76 (2007) 062112 [quant-ph/0701074] [INSPIRE].
D.E. Bruschi, J. Louko, E. Martín-Martínez, A. Dragan and I. Fuentes, The Unruh effect in quantum information beyond the single-mode approximation, Phys. Rev. A 82 (2010) 042332 [arXiv:1007.4670] [INSPIRE].
E. Martín-Martínez, L.J. Garay and J. León, Unveiling quantum entanglement degradation near a Schwarzschild black hole, Phys. Rev. D 82 (2010) 064006 [arXiv:1006.1394] [INSPIRE].
D.E. Bruschi, A. Dragan, I. Fuentes and J. Louko, Particle and anti-particle bosonic entanglement in non-inertial frames, Phys. Rev. D 86 (2012) 025026 [arXiv:1205.5296] [INSPIRE].
M.-R. Hwang, D. Park and E. Jung, Tripartite entanglement in noninertial frame, Phys. Rev. A 83 (2001) 012111 [arXiv:1010.6154] [INSPIRE].
S. Harikrishnan, S. Jambulingam, P.P. Rohde and C. Radhakrishnan, Accessible and inaccessible quantum coherence in relativistic quantum systems, Phys. Rev. A 105 (2022) 052403 [arXiv:2107.02490] [INSPIRE].
S.-M. Wu, H.-S. Zeng and H.-M. Cao, Quantum coherence and distribution of N-partite bosonic fields in noninertial frame, Class. Quant. Grav. 38 (2021) 185007 [arXiv:2201.00986] [INSPIRE].
E. Martín-Martínez and I. Fuentes, Redistribution of particle and anti-particle entanglement in non-inertial frames, Phys. Rev. A 83 (2011) 052306 [arXiv:1102.4759] [INSPIRE].
J. Chang and Y. Kwon, Entanglement behavior of quantum states of fermionic systems in an accelerated frame, Phys. Rev. A 85 (2012) 032302.
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 (2018) 022320 [INSPIRE].
A.J. Torres-Arenas, Q. Dong, G.-H. Sun, W.-C. Qiang and S.-H. Dong, Entanglement measures of W-state in noninertial frames, Phys. Lett. B 789 (2019) 93 [arXiv:1810.03951] [INSPIRE].
J. Wang, J. Deng and J. Jing, Classical correlation and quantum discord sharing of Dirac fields in noninertial frames, Phys. Rev. A 81 (2010) 052120 [arXiv:0912.4129] [INSPIRE].
S.-M. Wu and H.-S. Zeng, Genuine tripartite nonlocality and entanglement in curved spacetime, Eur. Phys. J. C 82 (2022) 4 [arXiv:2201.02333] [INSPIRE].
S.-M. Wu, Y.-T. Cai, W.-J. Peng and H.-S. Zeng, Genuine N-partite entanglement and distributed relationships in the background of dilation black holes, Eur. Phys. J. C 82 (2022) 412 [arXiv:2205.03662] [INSPIRE].
Q. Pan and J. Jing, Hawking radiation, entanglement and teleportation in background of an asymptotically flat static black hole, Phys. Rev. D 78 (2008) 065015 [arXiv:0809.0811] [INSPIRE].
B.N. Esfahani, M. Shamirzai and M. Soltani, Reduction of entanglement degradation and teleportation improvement in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 84 (2011) 025024 [arXiv:1010.5118] [INSPIRE].
J. He, S. Xu and L. Ye, Measurement-induced-nonlocality for Dirac particles in Garfinkle-Horowitz-Strominger dilation space-time, Phys. Lett. B 756 (2016) 278 [INSPIRE].
S. Xu, X.-K. Song, J.-D. Shi and L. Ye, How the Hawking effect affects multipartite entanglement of Dirac particles in the background of a Schwarzschild black hole, Phys. Rev. D 89 (2014) 065022 [INSPIRE].
J. Wang, J. Jing and H. Fan, Quantum discord and measurement-induced disturbance in the background of dilaton black holes, Phys. Rev. D 90 (2014) 025032 [arXiv:1408.0080] [INSPIRE].
J. Shi, J. Chen, J. He, T. Wu and L. Ye, Inevitable degradation and inconsistency of quantum coherence in a curved space-time, Quantum Inf. Process. 18 (2019) 300.
S. Kanno, J.P. Shock and J. Soda, Entanglement negativity in the multiverse, JCAP 03 (2015) 015 [arXiv:1412.2838] [INSPIRE].
S. Kanno, J.P. Shock and J. Soda, Quantum discord in de Sitter space, Phys. Rev. D 94 (2016) 125014 [arXiv:1608.02853] [INSPIRE].
J. Wang, C. Wen, S. Chen and J. Jing, Generation of genuine tripartite entanglement for continuous variables in de Sitter space, Phys. Lett. B 800 (2020) 135109 [arXiv:1911.05278] [INSPIRE].
C. Wen, J. Wang and J. Jing, Quantum steering for continuous variable in de Sitter space, Eur. Phys. J. C 80 (2020) 78 [arXiv:1901.04180] [INSPIRE].
J. Maldacena and G.L. Pimentel, Entanglement entropy in de Sitter space, JHEP 02 (2013) 038 [arXiv:1210.7244] [INSPIRE].
S. Kanno, J. Murugan, J.P. Shock and J. Soda, Entanglement entropy of α-vacua in de Sitter space, JHEP 07 (2014) 072 [arXiv:1404.6815] [INSPIRE].
A. Albrecht, S. Kanno and M. Sasaki, Quantum entanglement in de Sitter space with a wall, and the decoherence of bubble universes, Phys. Rev. D 97 (2018) 083520 [arXiv:1802.08794] [INSPIRE].
M. Sasaki, T. Tanaka and K. Yamamoto, Euclidean vacuum mode functions for a scalar field on open de Sitter space, Phys. Rev. D 51 (1995) 2979 [gr-qc/9412025] [INSPIRE].
M.O. Scully and M.S. Zubairy, Quantum optics, Cambridge University Press, Cambridge, U.K. (1997).
G. Mahler and V.A. Weberruß Quantum networks, Springer-Verlag, Berlin, Heidelberg, Germany (1995).
H. Xu et al., Experimental quantification of coherence of a tunable quantum detector, Phys. Rev. Lett. 125 (2020) 060404.
Y.-T. Wang et al., Directly measuring the degree of quantum coherence using interference fringes, Phys. Rev. Lett. 118 (2017) 020403.
Z. Tian, J. Jing and A. Dragan, Analog cosmological particle generation in a superconducting circuit, Phys. Rev. D 95 (2017) 125003 [arXiv:1702.00693] [INSPIRE].
J. Steinhauer et al., Analogue cosmological particle creation in an ultracold quantum fluid of light, Nature Commun. 13 (2022) 2890 [arXiv:2102.08279] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2207.11721
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Wu, SM., Wang, CX., Liu, DD. et al. Would quantum coherence be increased by curvature effect in de Sitter space?. J. High Energ. Phys. 2023, 115 (2023). https://doi.org/10.1007/JHEP02(2023)115
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2023)115