The effects of system–environment correlations on heat transport and quantum entanglement via collision models

  • Zhong-Xiao ManEmail author
  • Qi Zhang
  • Yun-Jie Xia


By means of collision models, we study the effects of system–environment correlations (SECs) on the heat transport and quantum entanglement in both transient and steady-state regimes. In the considered models, the reservoirs are simulated through two chains of particles whose nearest-neighbor collisions induce the SECs. In the first model, the system is a qubit connecting two independent reservoirs with different temperatures. We show that the heat currents exhibit oscillations and even reversed flows from the cold reservoir to the hot one depending on intracollision strengths of reservoir particles. In the stationary regime, we observe a nonlinear relation between heat currents and intracollision strengths, which can be accounted for by the established steady-state SECs. In our second model, the system contains two interacting qubits and we show that the initial entanglement of the system either vanishes within finite steps of collisions or recovers from disappearing and retains nonzero value. The combined regions of relevant parameters that sustain steady-state entanglement are presented. We also present a method to enhance the steady-state entanglement by enlarging temperature differences of the two reservoirs.


Collision model Heat current Quantum entanglement 



This work is supported by National Natural Science Foundation (China) under Grant Nos. 11574178 and 61675115, Shandong Provincial Natural Science Foundation (China) under Grant No. ZR2016JL005, and Taishan Scholar Project of Shandong Province (China) under Grant No. tsqn201812059.


  1. 1.
    Gemma, G., Michel, M., Mahler, G.: Quantum Thermodynamics. Springer, New York (2004)Google Scholar
  2. 2.
    Uzdin, R., Levy, A., Kosloff, R.: Equivalence of quantum heat machines, and quantum-thermodynamic signatures. Phys. Rev. X 5, 031044 (2015)Google Scholar
  3. 3.
    Goold, J., Huber, M., Riera, A., del Rio, L., Skrzypczyk, P.: The role of quantum information in thermodynamics-a topical review. J. Phys. A Math. Theor. 49, 143001 (2016)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Vinjanampathy, S., Anders, J.: Quantum thermodynamics. Contemp. Phys. 57, 545 (2016)ADSCrossRefGoogle Scholar
  5. 5.
    Allahverdyan, A.E., Nieuwenhuizen, T.M.: Extraction of work from a single thermal bath in the quantum regime. Phys. Rev. Lett. 85, 1799 (2000)ADSCrossRefGoogle Scholar
  6. 6.
    Kieu, T.D.: The second law, maxwell’s demon, and work derivable from quantum heat engines. Phys. Rev. Lett. 93, 140403 (2004)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Leggio, B., Bellomo, B., Antezza, M.: Quantum thermal machines with single nonequilibrium environments. Phys. Rev. A 91, 012117 (2015)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Malabarba, A.S.L., Short, A.J., Kammerlander, P.: Clockdriven quantum thermal engines. New J. Phys. 17, 045027 (2015)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Alicki, R., Gelbwaser-Klimovsky, D.: Non-equilibrium quantum heat machines. New J. Phys. 17, 115012 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    Tonner, F., Mahler, G.: Autonomous quantum thermodynamic machines. Phys. Rev. E 72, 066118 (2005)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Henrich, M.J., Mahler, G., Michel, M.: Driven spin systems as quantum thermodynamic machines: fundamental limits. Phys. Rev. E 75, 051118 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    Azimi, M., Chotorlishvili, L., Mishra, S.K., Vekua, T., Hubner, W., Berakdar, J.: Quantum otto heat engine based on a multiferroic chain working substance. New J. Phys. 16, 063018 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Leggio, B., Antezza, M.: Otto engine beyond its standard quantum limit. Phys. Rev. E 93, 022122 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    Quan, H.T., Liu, Y.X., Sun, C.P., Nori, F.: Quantum thermodynamic cycles and quantum heat engines. Phys. Rev. E 76, 031105 (2007)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Zagoskin, A.M., Savelev, S., Nori, F., Kusmartsev, F.V.: Squeezing as the source of inefficiency in the quantum otto cycle. Phys. Rev. B 86, 014501 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    Linden, N., Popescu, S., Skrzypczyk, P.: How small can thermal machines be? The smallest possible refrigerator. Phys. Rev. Lett. 105, 130401 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    Correa, L.A., Palao, J.P., Adesso, G., Alonso, D.: Performance bound for quantum absorption refrigerators. Phys. Rev. E 87, 042131 (2013)ADSCrossRefGoogle Scholar
  18. 18.
    Brunner, N., Huber, M., Linden, N., Popescu, S., Silva, R., Skrzypczyk, P.: Entanglement enhances cooling in microscopic quantum refrigerators. Phys. Rev. E 89, 032115 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    Kosloff, R., Geva, E., Gordon, J.M.: Quantum refrigerators in quest of the absolute zero. J. Appl. Phys. 87, 8093 (2000)ADSCrossRefGoogle Scholar
  20. 20.
    Brask, J.B., Brunner, N.: Small quantum absorption refrigerator in the transient regime: time scales, enhanced cooling, and entanglement. Phys. Rev. E 92, 062101 (2015)ADSCrossRefGoogle Scholar
  21. 21.
    Silva, R., Skrzypczyk, P., Brunner, N.: Small quantum absorption refrigerator with reversed couplings. Phys. Rev. E 92, 012136 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    Yu, C.S., Zhu, Q.Y.: Re-examining the self-contained quantum refrigerator in the strong-coupling regime. Phys. Rev. E 90, 052142 (2014)ADSCrossRefGoogle Scholar
  23. 23.
    Man, Z.X., Xia, Y.J.: Smallest quantum thermal machine: the effect of strong coupling and distributed thermal tasks. Phys. Rev. E 96, 012122 (2017)ADSCrossRefGoogle Scholar
  24. 24.
    He, Z.C., Huang, X.Y., Yu, C.S.: Enabling the self-contained refrigerator to work beyond its limits by filtering the reservoirs. Phys. Rev. E 96, 052126 (2017)ADSCrossRefGoogle Scholar
  25. 25.
    Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Nicacio, F., Ferraro, A., Imparato, A., Paternostro, M., Semiao, F.L.: Thermal transport in out-of-equilibrium quantum harmonic chains. Phys. Rev. E 91, 042116 (2015)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Oviedo-Casado, S., Prior, J., Chin, A.W., Rosenbach, R., Huelga, S.F., Plenio, M.B.: Phase-dependent exciton transport and energy harvesting from thermal environments. Phys. Rev. A 93, 02010 (2016)CrossRefGoogle Scholar
  28. 28.
    Werlang, T., Marchiori, M.A., Cornelio, M.F., Valente, D.: Optimal rectification in the ultrastrong coupling regime. Phys. Rev. E 89, 062109 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    Ordonez-Miranda, J., Ezzahri, Y., Joulain, K.: Quantum thermal diode based on two interacting spinlike systems under different excitations. Phys. Rev. E 95, 022128 (2017)ADSCrossRefGoogle Scholar
  30. 30.
    Werlang, T., Valente, D.: Heat transport between two pure-dephasing reservoirs. Phys. Rev. E 91, 012143 (2015)ADSCrossRefGoogle Scholar
  31. 31.
    Man, Z.X., An, N.B., Xia, Y.J.: Controlling heat flows among three reservoirs asymmetrically coupled to two two-level systems. Phys. Rev. E 94, 042135 (2016)ADSCrossRefGoogle Scholar
  32. 32.
    Rau, J.: Relaxation phenomena in spin and harmonic oscillator systems. Phys. Rev. 129, 1880 (1963)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Scarani, V., Ziman, M., Stelmachovic, P., Gisin, N., Buzek, V.: Thermalizing quantum machines: dissipation and entanglement. Phys. Rev. Lett. 88, 097905 (2002)ADSCrossRefGoogle Scholar
  34. 34.
    Ziman, M., Stelmachovic, P., Buzek, V., Hillery, M., Scarani, V., Gisin, N.: Diluting quantum information: an analysis of information transfer in system–reservoir interactions. Phys. Rev. A 65, 042105 (2002)ADSCrossRefGoogle Scholar
  35. 35.
    Ciccarello, F., Palma, G.M., Giovannetti, V.: Collisionmodel-based approach to non-markovian quantum dynamics. Phys. Rev. A 87, 040103 (2013)ADSCrossRefGoogle Scholar
  36. 36.
    Kretschmer, S., Luoma, K., Strunz, W.T.: Collision model for non-markovian quantum dynamics. Phys. Rev. A 94, 012106 (2016)ADSCrossRefGoogle Scholar
  37. 37.
    Cakmak, B., Pezzutto, M., Paternostro, M., Mustecaplioglu, O.E.: Non-Markovianity, coherence, and system–environment correlations in a long-range collision model. Phys. Rev. A 96, 022109 (2017)ADSCrossRefGoogle Scholar
  38. 38.
    Lorenzo, S., Ciccarello, F., Palma, G.M.: Composite quantum collision models. Phys. Rev. A 96, 032107 (2017)ADSCrossRefGoogle Scholar
  39. 39.
    Filippov, S.N., Piilo, J., Maniscalco, S., Ziman, M.: Divisibility of quantum dynamical maps and collision models. Phys. Rev. A 96, 032111 (2017)ADSCrossRefGoogle Scholar
  40. 40.
    McCloskey, R., Paternostro, M.: Non-Markovianity and system-environment correlations in a microscopic collision model. Phys. Rev. A 89, 052120 (2014)ADSCrossRefGoogle Scholar
  41. 41.
    Bernardes, N.K., Carvalho, A.R.R., Monken, C.H., Santos, M.F.: Environmental correlations and Markovian to non-Markovian transitions in collisional model. Phys. Rev. A 90, 032111 (2014)ADSCrossRefGoogle Scholar
  42. 42.
    Jin, J., Yu, C.S.: Non-markovianity in the collision model with environmental block. New J. Phys. 20, 053026 (2018)ADSCrossRefGoogle Scholar
  43. 43.
    Jin, J., Giovannetti, V., Fazio, R., Sciarrino, F., Mataloni, P., Crespi, A., Osellame, R.: All-optical non-Markovian stroboscopic quantum simulator. Phys. Rev. A 91, 012122 (2015)ADSCrossRefGoogle Scholar
  44. 44.
    Cuevas, Á., Geraldi, A., Liorni, C., Diego Bonavena, L., De Pasquale, A., Sciarrino, F., Giovannetti, V., Mataloni, P.: All optical implementation of collision-based evolutions of open quantum systems (2018). arXiv:1809.01922 [quant-ph]
  45. 45.
    Man, Z.X., Xia, Y.J., Franco, R.L.: Temperature effects on quantum non-Markovianity via collision models. Phys. Rev. A 97, 062104 (2015)ADSCrossRefGoogle Scholar
  46. 46.
    Lorenzo, S., McCloskey, R., Ciccarello, F., Paternostro, M., Palma, G.M.: Landauer’s principle in multipartite open quantum system dynamics. Phys. Rev. Lett. 115, 120403 (2015)ADSCrossRefGoogle Scholar
  47. 47.
    Lorenzo, S., Farace, A., Ciccarello, F., Palma, G.M., Giovannetti, V.: Heat flux and quantum correlations in dissipative cascaded systems. Phys. Rev. A 91, 022121 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    Pezzutto, M., Paternostro, M., Omar, Y.: Implications of non-markovian quantum dynamics for the landauer bound. New J. Phys. 18, 123018 (2016)ADSCrossRefGoogle Scholar
  49. 49.
    Li, L., Zou, J., Li, H., Xu, B.M., Wang, Y.M., Shao, B.: Effect of coherence of nonthermal reservoirs on heat transport in a microscopic collision model. Phys. Rev. E 97, 022111 (2018)ADSCrossRefGoogle Scholar
  50. 50.
    Chiara, G.D., Landi, G., Hewgill, A., Reid, B., Ferraro, A., Roncaglia, A.J., Antezza, M.: Reconciliation of quantum local master equations with thermodynamics. New J. Phys. 20, 113024 (2018)CrossRefGoogle Scholar
  51. 51.
    Watanabe, S.: Information theoretical Analysis of Multivariate Correlation. IBM J. Res. Dev. 4, 66 (1960)MathSciNetCrossRefGoogle Scholar
  52. 52.
    Kumar, A.: Multiparty quantum mutual information: an alternative definition. Phys. Rev. A 96, 012332 (2017)ADSCrossRefGoogle Scholar
  53. 53.
    Hu, M.L., Fan, H.: Quantum coherence of multiqubit states in correlated noisy channels (2018). arXiv:1812.04385v1 [quant-ph]
  54. 54.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2007)zbMATHGoogle Scholar
  55. 55.
    Arnesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in the 1D heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)ADSCrossRefGoogle Scholar
  56. 56.
    Wang, X.G.: Entanglement in the quantum heisenberg XY model. Phys. Rev. A 64, 012313 (2001)ADSCrossRefGoogle Scholar
  57. 57.
    Gunlycke, D., Kendon, V.M., Vedral, V., Bose, S.: Thermal concurrence mixing in a one-dimensional ising model. Phys. Rev. A 64, 042302 (2001)ADSCrossRefGoogle Scholar
  58. 58.
    Eisler, V., Zimboras, Z.: Entanglement in the XX spin chain with an energy current. Phys. Rev. A 71, 042318 (2005)ADSCrossRefGoogle Scholar
  59. 59.
    Quiroga, L., Rodrguez, F.J., Ramrez, M.E., Pars, R.: Nonequilibrium thermal entanglement. Phys. Rev. A 75, 032308 (2007)ADSCrossRefGoogle Scholar
  60. 60.
    Sinaysky, I., Petruccione, F., Burgarth, D.: Dynamics of nonequilibrium thermal entanglement. Phys. Rev. A 78, 062301 (2008)ADSCrossRefGoogle Scholar
  61. 61.
    Huang, X.L., Guo, J.L., Yi, X.X.: Nonequilibrium thermal entanglement in a three-qubit XX model. Phys. Rev. A 80, 054301 (2009)ADSCrossRefGoogle Scholar
  62. 62.
    Brask, J.B., Haack, G., Brunner, N., Huber, M.: Autonomous quantum thermal machine for generating steady-state entanglement. New J. Phys. 17, 113029 (2015)ADSCrossRefGoogle Scholar
  63. 63.
    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Physics and Physical Engineering, Shandong Provincial Key Laboratory of Laser Polarization and Information TechnologyQufu Normal UniversityQufuChina

Personalised recommendations