Abstract
We provide a method to prepare the freezing quantum state for quantum coherence via unitary operations. The initial product state consists of the control qubit and target qubit; when it satisfies certain conditions, the initial product state converts into the particular Bell diagonal state under the unitary operations, which have the property of freezing of quantum coherence under quantum channels. We calculate the frozen quantum coherence and corresponding quantum correlations, and find that the quantities are determined by the control qubit only when the freezing phenomena occur.
Similar content being viewed by others
References
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Giovannetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330 (2004)
Demkowicz-Dobrzański, R., Maccone, L.: Using entanglement against noise in quantum metrology. Phys. Rev. Lett. 113, 250801 (2014)
Giovannetti, V., Lloyd, S., Maccone, L.: Advances in quantum metrology. Nat. Photon. 5, 222 (2011)
Li, C., Chen, X., Li, S., Sun, F.: Correction of the second-order degree of coherence measurement. Chin. Opt. Lett. 14, 072701 (2016)
Asbóth, J.K., Calsamiglia, J., Ritsch, H.: Computable measure of nonclassicality for light. Phys. Rev. Lett. 94, 173602 (2005)
Streltsov, A., Singh, U., Dhar, H.S., Bera, M.N., Adesso, G.: Measuring quantum coherence with entanglement. Phys. Rev. Lett. 115, 020403 (2015)
Ford, L.H.: Quantum coherence effects and the second law of thermodynamics. Proc. R. Soc. A 364, 227 (1978)
Correa, L.A., Palao, J.P., Alonso, D., Adesso, G.: Quantum-enhanced absorption refrigerators. Sci. Rep. 4, 3949 (2014)
Roßnagel, J., Abah, O., Schmidt-Kaler, F., Singer, K., Lutz, E.: Nanoscale heat engine beyond the carnot limit. Phys. Rev. Lett. 112, 030602 (2014)
Lostaglio, M., Jennings, D., Rudolph, T.: Description of quantum coherence in thermodynamic processes requires constraints beyond free energy. Nat. Commun. 6, 6383 (2015)
Åberg, J.: Catalytic coherence. Phys. Rev. Lett. 113, 150402 (2014)
Plenio, M., Huelga, S.: Dephasing assisted transport: quantum networks and biomolecules. New J. Phys. 10, 113019 (2008)
Rebentrost, P., Mohseni, M., Aspuru-Guzik, A.: Role of quantum coherence and environmental fluctuations in chromophoric energy transport. J. Phys. Chem. B 113, 9942 (2009)
Li, C.M., Lambert, N., Chen, Y.N., Chen, G.Y., Nori, F.: Witnessing quantum coherence: from solid-state to biological systems. Sci. Rep. 2, 885 (2012)
Huelga, S.F., Plenio, M.B.: Vibrations, quanta and biology. Contemp. Phys. 54, 181 (2013)
Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)
Levi, F., Mintert, F.: A quantitative theory of coherent delocalization. New J. Phys. 16, 033007 (2014)
Marvian, I., Spekkens, R.W.: The theory of manipulations of pure state asymmetry: I. basic tools, equivalence classes and single copy transformations. New J. Phys. 15, 033001 (2013)
Bromley, T.R., Cianciaruso, M., Adesso, G.: Frozen quantum coherence. Phys. Rev. Lett. 114, 210401 (2015)
Ma, J., Yadin, B., Girolami, D., Vedral, V., Gu, M.: Converting coherence to quantum correlations. Phys. Rev. Lett. 116, 160407 (2016)
Yao, Y., Xiao, X., Ge, L., Sun, C.P.: Quantum coherence in multipartite systems. Phys. Rev. A 92, 022112 (2015)
Xi, Z., Li, Y., Fan, H.: Quantum coherence and correlations in quantum system. Sci. Rep. 5, 10922 (2015)
Bennett, C.H., Divincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824 (1996)
Vedral, V., Plenio, M.B., Rippin, M.A., Knight, P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275 (1997)
Vedral, V., Plenio, M.B.: Entanglement measures and purification procedures. Phys. Rev. A 57, 1619 (1998)
Vidal, G.: Entanglement monotones. J. Mod. Opt. 47, 355 (2000)
Plenio, M.B., Virmani, S.: Critical phenomena and the capacity of quantum channels with memory. Quantum Inf. Comput. 7, 1 (2007)
Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)
Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)
Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011)
Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)
Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)
Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)
Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A 34, 6899 (2001)
Oppenheim, J., Horodecki, M., Horodecki, P., Horodecki, R.: Thermodynamical approach to quantifying quantum correlations. Phys. Rev. Lett. 89, 180402 (2002)
Groisman, B., Popescu, S., Winter, A.: On the quantum, classical and total amount of correlations in a quantum state. Phys. Rev. A 72, 032317 (2005)
Acknowledgements
We acknowledge the financial support by the National Natural Science Foundation (China) under Grant Nos. 61675115, 11647171, 11574178, and 11304179.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Yang, LW., Man, ZX., Zhang, YJ. et al. Preparation of freezing quantum state for quantum coherence. Quantum Inf Process 17, 127 (2018). https://doi.org/10.1007/s11128-018-1889-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-018-1889-7