Abstract
In this paper, we examine how finite time disentanglement can be manipulated for the quantum system out of thermal equilibrium. To this aim, we employ the Markovian master equation approach to find the rate equations and Wootter’s concurrence to analyze out of thermal equilibrium entanglement dynamics for Dicke bases. The effect of super- and sub-radiant rates on entanglement sudden death is examined for different classes of X-states. It is found that the shorter dark period is achieved at a higher transition rate of a super-radiant state. This approach allows us to analyze the further applications of quantum information technologies.









Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data Availability
No datasets were generated or analysed during the current study.
References
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865 (2009)
Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40(8), 4277 (1989)
Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80(2), 517 (2008)
Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895 (1993)
Pan, J.W., Bouwmeester, D., Weinfurter, H., Zeilinger, A.: Experimental entanglement swapping: entangling photons that never interacted. Phys. Rev. Lett. 80(18), 3891 (1998)
Bennett, C.H., Wiesner, S.J.: Communication via one-and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69(20), 2881 (1992)
Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81(3), 1301 (2009)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67(6), 661 (1991)
Nielsen, M.A., Chuang, I.L.: Quantum Information and Quantum Computation, vol. 2 (2000)
Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93(14), 140404 (2004)
Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323(5914), 598–601 (2009)
Wang, F., Hou, P.Y., Huang, Y.Y., Zhang, W.G., Ouyang, X.L., Wang, X., Duan, L.M.: Observation of entanglement sudden death and rebirth by controlling a solid-state spin bath. Phys. Rev. B 98(6), 064306 (2018)
Ficek, Z., Tanaś, R.: Dark periods and revivals of entanglement in a two-qubit system. Phys. Rev. A 74(2), 024304 (2006)
Qian, X.F., Eberly, J.H.: Initial conditions and entanglement sudden death. Phys. Lett. A 376(45), 2931–2934 (2012)
Liu, R.F., Chen, C.C.: Role of the Bell singlet state in the suppression of disentanglement. Phys. Rev. A 74(2), 024102 (2006)
Roszak, K., Machnikowski, P.: Publisher’s Note: Complete disentanglement by partial pure dephasing [Phys. Rev. A73, 022313 (2006)]. Phys. Rev. A 73(2), 029906 (2006)
Shaukat, M.I., Shaheen, A., Toor, A.H.: Early stage disentanglement and non-Markovianity. J. Mod. Opt. 60(21), 1937–1948 (2013)
Shaukat, M.I.: Entanglement sudden death with quasi-static approximation. Eur. Phys. J. Plus 137(2), 1–9 (2022)
Shaukat, M.I., Castro, E.V., Terças, H.: Entanglement sudden death and revival in quantum dark-soliton qubits. Phys. Rev. A 98(2), 022319 (2018)
Abdel-Khalek, S., Barzanjeh, S., Eleuch, H.: Entanglement sudden death and sudden birth in semiconductor microcavities. Int. J. Theor. Phys. 50, 2939–2950 (2011)
Su, X.Q., Wang, A.M., San Ma, X., Qiu, L.: Entanglement sudden death in a spin channel. J. Phys. A Math. Theor. 40(37), 11385 (2007)
Ali, M., Alber, G., Rau, A.R.P.: Manipulating entanglement sudden death of two-qubit X-states in zero-and finite-temperature reservoirs. J. Phys. B At. Mol. Opt. Phys. 42(2), 025501 (2008)
Pan, C.N., Fang, J.S., Fang, M.F.: Entanglement dynamics of two-qubit systems in different quantum noises. Chin. Phys. B 20(2), 020304 (2011)
Tchoffo, M., Kenfack, L.T., Fouokeng, G.C., Fai, L.C.: Quantum correlations dynamics and decoherence of a three-qubit system subject to classical environmental noise. Eur. Phys. J. Plus 131, 1–18 (2016)
Yang, C.J., An, J.H., Yang, W., Li, Y.: Generation of stable entanglement between two cavity mirrors by squeezed-reservoir engineering. Phys. Rev. A 92(6), 062311 (2015)
Pedram, A., Müstecaplıoǧlu, Ö.E.: An Overview: Steady-State Quantum Entanglement via Reservoir Engineering. arXiv preprint arXiv:2303.00490 (2023)
Kwiat, P.G., Barraza-Lopez, S., Stefanov, A., Gisin, N.: Experimental entanglement distillation and ‘hidden’ non-locality. Nature 409(6823), 1014–1017 (2001)
Maniscalco, S., Francica, F.: RL Zaffino, N. Lo Gullo, and F. Plastina. Phys. Rev. Lett 100, 090503 (2008)
Agarwal, G.S.: Quantum Statistical Theories of Spontaneous Emission and Their Relation to Other Approaches. Springer, Berlin (2006)
Ficek, Z., Swain, S.: Quantum Interference and Coherence: Theory and Experiments, vol. 100. Springer, Berlin (2005)
Tayyab, A., Javed, S., Shaukat, M.I.: Superdense coding for V-shaped channel and cylindrical geometry. Phys. Scr. 98(9), 095109 (2023)
Almutairi, K., Tanaś, R., Ficek, Z.: Generating two-photon entangled states in a driven two-atom system. Phys. Rev. A 84(1), 013831 (2011)
Quiroga, L., Rodriguez, F.J., Ramirez, M.E., Paris, R.: Nonequilibrium thermal entanglement. Phys. Rev. A 75(3), 032308 (2007)
Sinaysky, I., Petruccione, F., Burgarth, D.: Dynamics of nonequilibrium thermal entanglement. Phys. Rev. A 78(6), 062301 (2008)
Huang, X.L., Guo, J.L., Yi, X.X.: Nonequilibrium thermal entanglement in a three-qubit X X model. Phys. Rev. A 80(5), 054301 (2009)
Linden, N., Popescu, S., Skrzypczyk, P.: How small can thermal machines be? The smallest possible refrigerator. Phys. Rev. Lett. 105(13), 130401 (2010)
Skrzypczyk, P., Brunner, N., Linden, N., Popescu, S.: The smallest refrigerators can reach maximal efficiency. J. Phys. A Math. Theor. 44(49), 492002 (2011)
Tacchino, F., Auffèves, A., Santos, M.F., Gerace, D.: Steady state entanglement beyond thermal limits. Phys. Rev. Lett. 120(6), 063604 (2018)
Bellomo, B., Antezza, M.: Creation and protection of entanglement in systems out of thermal equilibrium. New J. Phys. 15(11), 113052 (2013)
Bellomo, B., Antezza, M.: Steady entanglement out of thermal equilibrium. Europhys. Lett. 104(1), 10006 (2013)
Obrecht, J.M., Wild, R.J., Antezza, M., Pitaevskii, L.P., Stringari, S., Cornell, E.A.: Measurement of the temperature dependence of the Casimir–Polder force. Phys. Rev. Lett. 98(6), 063201 (2007)
Dicke, R.H.: Coherence in spontaneous radiation processes. Phys. Rev. 93(1), 99 (1954)
Parker, S., Bose, S., Plenio, M.B.: Entanglement quantification and purification in continuous-variable systems. Phys. Rev. A 61(3), 032305 (2000)
Moroder, T., Bancal, J.D., Liang, Y.C., Hofmann, M., Gühne, O.: Device-independent entanglement quantification and related applications. Phys. Rev. Lett. 111(3), 030501 (2013)
Fadel, M., Usui, A., Huber, M., Friis, N., Vitagliano, G.: Entanglement quantification in atomic ensembles. Phys. Rev. Lett. 127(1), 010401 (2021)
Abebe, T., Gemechu, N., Shogile, K., Hailemariam, S., Gashu, C., Adisu, S.: Entanglement quantification using various inseparability criteria for correlated photons. Rom. J. Phys. 65(3–4), 107 (2020)
Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80(10), 2245 (1998)
Eltschka, C., Siewert, J.: Negativity as an estimator of entanglement dimension. Phys. Rev. Lett. 111(10), 100503 (2013)
Miranowicz, A., Ishizaka, S.: Closed formula for the relative entropy of entanglement. Phys. Rev. A 78(3), 032310 (2008)
Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23(15), 880 (1969)
Ishizaka, S., Hiroshima, T.: Maximally entangled mixed states under nonlocal unitary operations in two qubits. Phys. Rev. A 62(2), 022310 (2000)
De Chiara, G., 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(11), 113024 (2018)
Yashodamma, K.O., Geetha, P.J., Sudha: Effectiveness of depolarizing noise in causing sudden death of entanglement. Quantum Inf. Process. 13, 2551–2565 (2014)
Zhang, W.M.: Exact master equation and general non-Markovian dynamics in open quantum systems. Eur. Phys. J. Spec. Top. 227, 1849–1867 (2019)
Vijayan, J., Piotrowski, J., Gonzalez-Ballestero, C., Weber, K., Romero-Isart, O., Novotny, L.: Cavity-mediated long-range interactions in levitated optomechanics. Nat. Phys. 66, 1–6 (2024)
Luo, S., Fu, S.: Geometric measure of quantum discord. Phys. Rev. A 82(3), 034302 (2010)
Weinstein, Y.S.: Entanglement evolution in a five qubit error correction code. Quantum Inf. Process. 10, 533–542 (2011)
Author information
Authors and Affiliations
Contributions
Ansha Tayyab and Seerat Javed wrote the main manuscript. Ansha Tayyab prepared figures. Muzzamal Iqbal Shaukat supervised the research. All authors reviewed the manuscript.
Corresponding author
Ethics declarations
Conflicts of interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Tayyab, A., Javed, S. & Shaukat, M.I. Early-stage disentanglement out of thermal equilibrium. Quantum Inf Process 23, 249 (2024). https://doi.org/10.1007/s11128-024-04447-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-024-04447-1