Tripartite entanglement of Hawking radiation in dispersive model

[1] S. W. Hawking, Black hole explosions?, Nature (London) 248, 30 (1974).

[2] S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975).

[3] W. Unruh, Sonic analogue of black holes and the effects of high frequencies on black hole evaporation, Phys. Rev. D 51, 2827 (1995).

[4] R. Brout, S. Massar, R. Parentani, and P. Spindel, Hawking radiation without trans-Planckian frequencies, Phys. Rev. D 52, 4559 (1995).

[5] S. Corley and T. Jacobson, Hawking spectrum and high frequency dispersion., Phys. Rev. D 54, 1568 (1996).

[6] Y. Himemoto and T. Tanaka, Generalization of the model of Hawking radiation with modified high frequency dispersion relation, Phys. Rev. D 61, 064004 (2000).

[7] T. Jacobson, in Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect, Lect. Quantum Gravity (Springer-Verlag, New York, 2003), pp. 39–89.

[8] W. Unruh and R. Schützhold, Universality of the Hawking effect, Phys. Rev. D 71, 024028 (2005).

[9] J. Macher and R. Parentani, Black-hole radiation in Bose-Einstein condensates, Phys. Rev. A 80, 043601 (2009).

[10] J. Macher and R. Parentani, Black/white hole radiation from dispersive theories, Phys. Rev. D 79, 124008 (2009).

[11] S. J. Robertson, The theory of Hawking radiation in laboratory analogues, J. Phys. B 45, 163001 (2012).

[12] U. Leonhardt and S. Robertson, Analytical theory of Hawking radiation in dispersive media, New J. Phys. 14, 053003 (2012).

[13] A. Coutant, R. Parentani, and S. Finazzi, Black hole radiation with short distance dispersion, an analytical S-matrix approach, Phys. Rev. D 85, 024021 (2012).

[14] M. Hotta, R. Schützhold, and W. G. Unruh, Partner particles for moving mirror radiation and black hole evaporation, Phys. Rev. D 91, 124060 (2015).

[15] X. Busch and R. Parentani, Quantum entanglement in analogue Hawking radiation: When is the final state nonseparable?, Phys. Rev. D 89, 105024 (2014).

[16] A. Peres, Separability Criterion for Density Matrices, Phys. Rev. Lett. 77, 1413 (1996).

[17] P. Horodecki, Separability criterion and inseparable mixed states with positive partial transposition, Phys. Lett. A 232, 333 (1997).

[18] R. Simon, Peres-Horodecki Separability Criterion for Continuous Variable Systems, Phys. Rev. Lett. 84, 2726 (2000).

[19] P. R. Anderson, R. Balbinot, A. Fabbri, and R. Parentani, Gray-body factor and infrared divergences in 1D BEC acoustic black holes, Phys. Rev. D 90, 104044 (2014).

[20] P. R. Anderson, A. Fabbri, and R. Balbinot, Low frequency gray-body factors and infrared divergences: Rigorous results, Phys. Rev. D 91, 064061 (2015).

[21] A. Fabbri, R. Balbinot, and P. R. Anderson, Scattering coefficients and gray-body factor for 1D BEC acoustic black holes: Exact results, Phys. Rev. D 93, 064046 (2016).

[22] A. Recati, N. Pavloff, and I. Carusotto, Bogoliubov theory of acoustic Hawking radiation in Bose-Einstein condensates, Phys. Rev. A 80, 043603 (2009).

[23] G. Giedke and B. Kraus, Gaussian local unitary equivalence of n -mode Gaussian states and Gaussian transformations by local operations with classical communication, Phys. Rev. A 89, 012335 (2014).

[24] C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys. 84, 621 (2012).

[25] G. Vidal and R. Werner, Computable measure of entanglement, Phys. Rev. A 65, 032314 (2002).

[26] G. Adesso and F. Illuminati, Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems, New J. Phys. 8, 15 (2006).

[27] P. Kanti, J. Grain, and A. Barrau, Bulk and brane decay of a (4 þ n)-dimensional Schwarzschild-de Sitter black hole: Scalar radiation, Phys. Rev. D 71, 104002 (2005).

[28] M. Isoard, N. Milazzo, N. Pavloff, and O. Giraud, Bipartite and tripartite entanglement in a Bose-Einstein acoustic black hole, arXiv:2102.06175.