Abstract
We analytically study the dynamical behavior of the quantum coherence of a single-qubit coupled to a bosonic reservoir at zero temperature via plugging additional non-interacting qubits into the reservoir in both Markovian and non-Markovian regimes. The influences of detuning, memory effects and number of additional qubits on the dynamics of the quantum coherence are considered. It is found that, via increasing the number of the additional qubits in the reservoir, the quantum coherence can be preserved. Moreover, the method based on the combination of larger effective detuning, the stronger non-Markovian effects and the more number of additional qubits, can more effectively prevent the loss of the quantum coherence.
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Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)
Streltsov, A., Adesso, G., Plenio, M.B.: Quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2017)
Winter, A., Yang, D.: Operational resource theory of coherence. Phys. Rev. Lett. 116, 120404 (2016)
Giovannetti, V., Lloyd, S., Maccone, L.: Advances in quantum metrology. Nat. Photonics 5, 222–229 (2011)
Marvian, I., Spekkens, R.W.: How to quantify coherence: distinguishing speakable and unspeakable notions. Phys. Rev. A 94, 052324 (2016)
Plenio, M.B., Huelga, S.F.: Dephasing-assisted transport: quantum networks and biomolecules. New J. Phys. 10, 113019 (2008)
Lloyd, S.: Quantum coherence in biological systems. J. Phys.: Conf. Ser. 302, 012037 (2011)
Levi, F., Mintert, F.: A quantitative theory of coherent delocalization. New J. Phys. 16, 033007 (2014)
Huelga, S.F., Plenio, M.B.: Vibrations, quanta and biology. Contemp. Phys. 54, 181 (2013)
Lostaglio, M., Jennings, D., Rudolph, T.: Description of quantum coherence in thermodynamic processes requires constraints beyond free energy. Nat. Commun. 6, 6383 (2015)
Ćwikliński, P., Studziński, M., Horodecki, M., Oppenheim, J.: Limitations on the evolution of quantum coherences: Towards fully quantum second laws of thermodynamics. Phys. Rev. Lett. 115, 210403 (2015)
Misra, A., Singh, U., Bhattacharya, S., Pati, A.K.: Energy cost of creating quantum coherence. Phys. Rev. A 93, 052335 (2016)
Shi, H.-L., Liu, S.-Y., Wang, X.-H., Yang, W.-L., Yang, Z.-Y., Fan, H.: Coherence depletion in the Grover quantum search algorithm. Phys. Rev. A 95, 032307 (2017)
Hillery, M.: Coherence as a resource in decision problems: the Deutsch-Jozsa algorithm and a variation. Phys. Rev. A 93, 012111 (2016)
Matera, J.M., Egloff, D., Killoran, N., Plenio, M.B.: Coherent control of quantum systems as a resource theory. Quantum Sci. Technol. 1, 01LT01 (2016)
Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)
Napoli, C., Bromley, T.R., Cianciaruso, M., Piani, M., Johnston, N., Adesso, G.: Robustness of coherence: an operational and observable measure of quantum coherence. Phys. Rev. Lett. 116, 150502 (2016)
Rana, S., Parashar, P., Lewenstein, M.: Trace-distance measure of coherence. Phys. Rev. A 93, 012110 (2016)
Shao, L.H., Xi, Z.J., Fan, H., Li, Y.M.: Fidelity and trace-norm distances for quantifying coherence. Phys. Rev. A 91, 042120 (2015)
Chitambar, E., Streltsov, A., Rana, S., Bera, M.N., Adesso, G., Lewenstein, M.: Assisted distillation of quantum coherence. Phys. Rev. Lett. 116, 070402 (2016)
Girolami, D.: Observable measure of quantum coherence in finite dimensional systems. Phys. Rev. Lett. 113, 170401 (2014)
Werner, R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)
Streltsov, A., Singh, U., Dhar, H.S., Bera, M.N., Adesso, G.: Measuring quantum coherence with entanglement. Phys. Rev. Lett. 115, 020403 (2015)
Yuan, X., Zhou, H.Y., Cao, Z., Ma, X.F.: Intrinsic randomness as a measure of quantum coherence. Phys. Rev. A 92, 022124 (2015)
Xi, Z.J., Li, Y.M., Fan, H.: Quantum coherence and correlations in quantum system. Sci. Rep. 5, 10922 (2015)
Hu, X.Y., Fan, H.: Extracting quantum coherence via steering. Sci. Rep. 6, 34380 (2016)
Hu, X.Y., Milne, A., Zhang, B.Y., Fan, H.: Quantum coherence of steered states. Sci. Rep. 6, 19365 (2016)
Hu, X.Y.: Channels that do not generate coherence. Phys. Rev. A 94, 012326 (2016)
Liu, Z.W., Hu, X.Y., Lloyd, S.: Resource destroying maps. Phys. Rev. Lett. 118, 060502 (2017)
Singh, U., Bera, M.N., Misra, A., Pati, A.K.: Erasing quantum coherence: an operational approach. arXiv:1506.08186 (2015)
Kofman, A.G., Kurizki, G.: Acceleration of quantum decay processes by frequent observations. Nature (London) 405, 546–550 (2000)
Nourmandipour, A., Tavassoly, M.K., Rafiee, M.: Dynamics and protection of entanglement in n-qubit systems within Markovian and non-Markovian environments. Phys. Rev. A 93, 022327 (2016)
Ba An, N., Kim, J., Kim, K.: Nonperturbative analysis of entanglement dynamics and control for three qubits in a common lossy cavity. Phys. Rev. A 82, 032316 (2010)
Xiao, X., Li, Y., Zeng, K., Wu, C.: Robust entanglement preserving by detuning in non-Markovian regime. J. Phys. B: At. Mol. Opt. Phys. 42, 235502 (2009)
Bellomo, B., Lo Franco, R., Compagno, G.: Non-markovian effects on the dynamics of Entanglement. Phys. Rev. Lett. 99, 160502 (2007)
Mazzola, L., Maniscalco, S., Piilo, J., Suominen, K.-A., Garraway, B.M.: Sudden death and sudden birth of entanglement in common structured reservoirs. Phys. Rev. A 79, 042302 (2009)
Behzadi, N., Ahansaz, B., Ektesabi, A., Faizi, E.: Controlling speedup in open quantum systems through manipulation of system-reservoir bound states. Phys. Rev. A 95, 052121 (2017)
Behzadi, N., Ahansaz, B., Faizi, E.: Quantum coherence and entanglement preservation in Markovian and non-Markovian dynamics via additional qubits. Eur. Phys. J. D 71, 280 (2017)
Ba An, N., Kim, J., Kim, K.: Entanglement dynamics of three interacting two-level atoms within a common structured environment. Phys. Rev. A 84, 022329 (2011)
Ba An, N.: Protecting entanglement of atoms stored in a common nonperfect cavity without measurements. Phys. Lett. A 377, 2520–2523 (2013)
Flores, M.M., Galapon, E.A.: Two qubit entanglement preservation through the addition of qubits. Ann. Phys. 354, 21–30 (2015)
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant No. 11275064), the Natural Science Foundation of Hunan Province (Grant No. 2016JJ2045), Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education (QSQC1411) and Hunan Provincial Department of Education Natural Science Foundation General Project (Grant No. 16C0469).
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Wang, Gy., Jiang, Dk. Dynamics and Protection of the Relative Entropy of Coherence via Additional Non-interacting Qubits. Int J Theor Phys 58, 333–344 (2019). https://doi.org/10.1007/s10773-018-3934-9
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DOI: https://doi.org/10.1007/s10773-018-3934-9