Abstract
We adequately characterize the distillability of quantum coherence under the maximally incoherent operations (MIO) in the probabilistic distillation’s framework. In particular, we prove that every non-full-rank coherent state exhibits a nonzero probability in the task of probabilistic deterministic distillation. Moreover, we find that the maximal coherence, a computable coherence monotone under strictly incoherent operations (SIO), is a coherence monotone under incoherent operations (IO) and add the proof that the maximal coherence fulfills strong monotonicity under SIO. It is suggested that the maximal success probability of distillation from all coherent states whose density matrix does not contain any rank-one submatrix is less than 1 under IO and equals 0 under SIO. Finally, we present an explicit example for probabilistic distillation under IO and show that a class of non-full rank 3-dimensional states possesses the probabilistic distillability.
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References
Aberg, J.: Quantifying superposition. arXiv preprint arXiv:quant-ph/0612146 (2006)
Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113(14), 140401 (2014)
Brandao, F.G.S.L., Gour, G.: Reversible framework for quantum resource theories. Phys. Rev. Lett. 115(7), 070503 (2015)
Bu, K., Singh, U., Fei, S.M., et al.: Maximum relative entropy of coherence: an operational coherence measure. Phys. Rev. Lett. 119(15), 150405 (2017)
Chitambar, E., Gour, G.: Comparison of incoherent operations and measures of coherence. Phys. Rev. A 94(5), 052336 (2016)
Chitambar, E., Gour, G.: Critical examination of incoherent operations and a physically consistent resource theory of quantum coherence. Phys. Rev. Lett. 117(3), 030401 (2016)
Chitambar, E., Gour, G.: Quantum resource theories. Rev. Modern Phys. 91(2), 025001 (2019)
De Vicente, J.I., Streltsov, A.: Genuine quantum coherence. J. Phys. A Math. Theor. 50(4), 045301 (2016)
Du, S., Bai, Z., Guo, Y.: Conditions for coherence transformations under incoherent operations. Phys. Rev. A 91(5), 052120 (2015)
Fang, K., Wang, X., Lami, L., et al.: Probabilistic distillation of quantum coherence. Phys. Rev. Lett. 121(7), 070404 (2018)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (2012)
Hu, M.L., Hu, X., Wang, J., et al.: Quantum coherence and geometric quantum discord. Phys. Rep. 762, 1–100 (2018)
Lami, L.: Completing the grand tour of asymptotic quantum coherence manipulation. IEEE Trans. Inf. Theory 66(4), 2165–2183 (2020). https://doi.org/10.1109/TIT.2019.2945798
Lami, L., Regula, B., Adesso, G.: Generic bound coherence under strictly incoherent operations. Phys. Rev. Lett. 122(15), 150402 (2019)
Levi, F., Mintert, F.: A quantitative theory of coherent delocalization. New J. Phys. 16(3), 033007 (2014)
Liu, C.L., Zhou, D.L.: Deterministic coherence distillation. Phys. Rev. Lett. 123(7), 070402 (2019)
Luo, Y., Li, Y., Hsieh, M.H.: Inequivalent multipartite coherence classes and two operational coherence monotones. Phys. Rev. A 99(4), 042306 (2019)
Regula, B., Fang, K., Wang, X., et al.: One-shot coherence distillation. Phys. Rev. Lett. 121(1), 010401 (2018)
Shao, L.H., Xi, Z., Fan, H., et al.: Fidelity and trace-norm distances for quantifying coherence. Phys. Rev. A 91(4), 042120 (2015)
Streltsov, A., Adesso, G., Plenio, M.B.: Colloquium: quantum coherence as a resource. Rev. Mod. Phys. 89(4), 041003 (2017)
Torun, G., Lami, L., Adesso, G., et al.: Optimal distillation of quantum coherence with reduced waste of resources. Phys. Rev. A 99(1), 012321 (2019)
Winter, A., Yang, D.: Operational resource theory of coherence. Phys. Rev. Lett. 116(12), 120404 (2016)
Xi, Z., Li, Y., Fan, H.: Quantum coherence and correlations in quantum system. Sci. Rep. 5, 10922 (2015)
Yadin, B., Ma, J., Girolami, D., et al.: Quantum processes which do not use coherence. Phys. Rev. X 6(4), 041028 (2016)
Yu, X.D., Zhang, D.J., Xu, G.F., et al.: Alternative framework for quantifying coherence. Phys. Rev. A 94(6), 060302 (2016)
Yuan, X., Zhou, H., Cao, Z., et al.: Intrinsic randomness as a measure of quantum coherence. Phys. Rev. A 92(2), 022124 (2015)
Zhao, Q., Liu, Y., Yuan, X., et al.: One-shot coherence dilution. Phys. Rev. Lett. 120(7), 070403 (2018)
Zhao, Q., Liu, Y., Yuan, X., et al.: One-shot coherence distillation: towards completing the picture. IEEE Trans. Inf. Theory 10, 62 (2019)
Acknowledgements
We thank Chenming Bai, Yufeng Lian, and Shanshan Yuwen for fruitful discussions. This paper was supported by National Science Foundation of China (Grant No:11671244, 11271237), the Higher school Doctoral Subject Foundation of Ministry of Education of China (Grant No:20130202110001), the Central Universities (Grant No: GK202003070) and the National Natural Science Foundation of China (Grant No: 62001274).
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Li, P., Luo, Y. & Li, Y. Distillability for non-full-rank coherent states in the probabilistic framework. Quantum Inf Process 19, 374 (2020). https://doi.org/10.1007/s11128-020-02782-7
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DOI: https://doi.org/10.1007/s11128-020-02782-7