Symmetry-Like Relation of Relative Entropy Measure of Quantum Coherence
Abstract
1. Introduction
2. Preliminaries
3. Lower and Upper Bounds for the Relative Entropy of Coherence
4. The Relation between and
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
- Marius, N.; Selim, G. On the importance of parallelism for quantum computation and the concept of a universal computer. In Unconventional Computation; Calude, C.S., Dinneen, M.J., Păun, G., Pérez-Jímenez, M.J., Rozenberg, G., Eds.; Springer: Berlin/Heidelberg, Germany, 2005; Volume 3699, pp. 176–190. [Google Scholar]
- Paredes, B.; Verstraete, F.; Cirac, J.I. Exploiting quantum parallelism to simulate quantum random many-body systems. Phys. Rev. Lett. 2005, 93, 140501. [Google Scholar] [CrossRef] [PubMed]
- O’Leary, D.P.; Brennen, G.K.; Bullock, S.S. Parallelism for quantum computation with qudits. Phys. Rev. A 2006, 74, 032334. [Google Scholar] [CrossRef]
- Nielsen, M.A.; Chuang, I.L. Quantum Computation and Quantum Information; Cambridge University Press: Cambridge, UK, 2001. [Google Scholar]
- Rebentrost, P.; Mohseni, M.; Aspuru-Guzik, A. Role of quantum coherence and environmental fluctuations in chromophoric energy transport. J. Phys. Chem. B 2009, 113, 9942–9947. [Google Scholar] [CrossRef] [PubMed]
- Lloyd, S. Quantum coherence in biological systems. J. Phys. Conf. Ser. 2011, 302, 012037. [Google Scholar] [CrossRef]
- Li, C.M.; Lambert, N.; Chen, Y.N.; Chen, G.Y.; Nori, F. Witnessing quantum coherence: From solid-state to biological systems. Sci. Rep. 2012, 2, 885. [Google Scholar] [CrossRef]
- Huelga, S.; Plenio, M. Vibrations, quanta and biology. Contemp. Phys. 2013, 54, 181–207. [Google Scholar] [CrossRef]
- Plenio, M.B.; Huelga, S.F. Dephasing-assisted transport: Quantum networks and biomolecules. New J. Phys. 2008, 10, 113019. [Google Scholar] [CrossRef]
- Levi, F.; Mintert, F. A quantitative theory of coherent delocalization. New J. Phys. 2014, 16, 033007. [Google Scholar] [CrossRef]
- Vazquez, H.; Skouta, R.; Schneebeli, S.; Kamenetska, M.; Breslow, R.; Venkataraman, L.; Hybertsen, M.S. Probing the conductance superposition law in single-molecule circuits with parallel paths. Nat. Nanotechnol. 2012, 7, 663–667. [Google Scholar] [CrossRef]
- Karlstrom, O.; Linke, H.; Karlstrom, G.; Wacker, A. Increasing thermoelectric performance using coherent transport. Phys. Rev. B 2011, 84, 113415. [Google Scholar] [CrossRef]
- Giovannetti, V.; Lloyd, S.; Maccone, L. Advances in quantum metrology. Nat. Photonics 2011, 5, 222–229. [Google Scholar] [CrossRef]
- Giovannetti, V. Quantum-enhanced measurements: Beating the standard quantum limit. Science 2004, 306, 1330–1336. [Google Scholar] [CrossRef] [PubMed]
- Baumgratz, T.; Cramer, M.; Plenio, M.B. Quantifying coherence. Phys. Rev. Lett. 2014, 113, 140401. [Google Scholar] [CrossRef] [PubMed]
- Shao, L.H.; Xi, Z.J.; Fan, H.; Li, Y.M. Fidelity and trace norm distances for quantifying coherence. Phys. Rev. A 2014, 91, 042120. [Google Scholar] [CrossRef]
- 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. 2016, 116, 150502. [Google Scholar] [CrossRef]
- Streltsov, A.; Singh, U.; Dhar, H.S.; Bera, M.N.; Adesso, G. Measuring quantum coherence with entanglement. Phys. Rev. Lett. 2015, 115, 020403. [Google Scholar] [CrossRef]
- Winter, A.; Yang, D. Operational resource theory of coherence. Phys. Rev. Lett. 2016, 116, 120404. [Google Scholar] [CrossRef]
- Hu, M.L.; Fan, H. Relative quantum coherence, incompatibility, and quantum correlations of states. Phys. Rev. A 2017, 95, 052106. [Google Scholar] [CrossRef]
- Qi, X.; Gao, T.; Yan, F. Measuring coherence with entanglement concurrence. J. Phys. A Math. Theor. 2017, 50, 285301. [Google Scholar] [CrossRef]
- Rana, S.; Parashar, P.; Lewenstein, M. Trace-distance measure of coherence. Phys. Rev. A 2016, 93, 012110. [Google Scholar] [CrossRef]
- Chen, B.; Fei, S.M. Notes on modified trace distance measure of coherence. Quantum Inf. Comput. 2018, 17, 107. [Google Scholar] [CrossRef]
- Yu, X.D.; Zhang, D.J.; Xu, G.F.; Tong, D.M. Alternative framework for quantifying coherence. Phys. Rev. A 2016, 94, 060302. [Google Scholar] [CrossRef]
- Yao, Y.; Xiao, X.; Ge, L.; Sun, C.P. Quantum coherence in multipartite systems. Phys. Rev. A 2015, 92, 022112. [Google Scholar] [CrossRef]
- Streltsov, A. Genuine quantum coherence. J. Phys. A 2017, 50, 045301. [Google Scholar]
- Sun, Y.; Mao, Y.; Luo, S.L. From quantum coherence to quantum correlations. Europhys. Lett. 2017, 118, 60007. [Google Scholar] [CrossRef]
- Tan, K.C.; Kwon, H.; Park, C.Y.; Jeong, H. Unified view of quantum correlations and quantum coherence. Phys. Rev. A 2017, 96, 069905. [Google Scholar] [CrossRef]
- Guo, Y.; Goswami, S. Discordlike correlation of bipartite coherence. Phys. Rev. A 2017, 95, 062340. [Google Scholar] [CrossRef]
- Xi, Z.; Li, Y.; Fan, H. Quantum coherence and correlations in quantum system. Sci. Rep. 2015, 5, 10922. [Google Scholar] [CrossRef]
- Liu, F.; Li, F.; Chen, J.; Xing, W. Uncertainty-like relations of the relative entropy of coherence. Quantum Inf. Comput. 2017, 15, 3459–3465. [Google Scholar] [CrossRef]
- Radhakrishnan, C.; Parthasarathy, M.; Jambulingam, S.; Byrnes, T. Distribution of quantum coherence in multipartite systems. Phys. Rev. Lett. 2016, 116, 150504. [Google Scholar] [CrossRef]
- Xi, Z. Quantum coherence over the noisy quantum channels. Sci. China-Phys. Mech. Astron. 2015, 45, 030302. [Google Scholar] [CrossRef]
- Singh, U.; Bera, M.N.; Dhar, H.S.; Pati, A.K. Maximally coherent mixed states: Complementarity between maximal coherence and mixedness. Phys. Rev. A 2015, 91, 052115. [Google Scholar] [CrossRef]
- Liu, C.L.; Yu, X.D.; Xu, G.F.; Tong, D.M. Ordering states with coherence measures. Quantum Inf. Comput. 2016, 15, 4189–4201. [Google Scholar] [CrossRef]
- Bagan, E.; Bergou, J.A.; Cottrell, S.S.; Hillery, M. Relations between coherence and path information. Phys. Rev. Lett. 2016, 116, 160406. [Google Scholar] [CrossRef] [PubMed]
- Cheng, S.; Hall, M.J.W. Complementarity relations for quantum coherence. Phys. Rev. A 2015, 92, 042101. [Google Scholar] [CrossRef]
- Ma, J.; Yadin, B.; Girolami, D.; Vedral, V.; Gu, M. Converting coherence to quantum correlations. Phys. Rev. Lett. 2016, 116, 160407. [Google Scholar] [CrossRef]
- Rana, S.; Parashar, P.; Winter, A.J.; Lewenstein, M. Logarithmic coherence: Operational interpretation of ℓ1-norm coherence. Phys. Rev. A 2017, 96, 052336. [Google Scholar] [CrossRef]
- Hu, M.L.; Hu, X.Y.; Wang, J.C.; Peng, Y.; Zhang, Y.R.; Fan, H. Quantum coherence and geometric quantum discord. Phys. Rep. 2018, 762–764, 1–100. [Google Scholar] [CrossRef]
- Guo, Z.H.; Cao, H.X. Creating quantum correlation from coherence via incoherent quantum operations. J. Phys. A Math. Theor. 2019, 52, 265301. [Google Scholar] [CrossRef]
- Choi, M.D. Completely positive linear maps on complex matrices. Linear Algebra Appl. 1975, 10, 285–290. [Google Scholar] [CrossRef]
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhang, C.; Guo, Z.; Cao, H. Symmetry-Like Relation of Relative Entropy Measure of Quantum Coherence. Entropy 2020, 22, 297. https://doi.org/10.3390/e22030297
Zhang C, Guo Z, Cao H. Symmetry-Like Relation of Relative Entropy Measure of Quantum Coherence. Entropy. 2020; 22(3):297. https://doi.org/10.3390/e22030297
Chicago/Turabian StyleZhang, Chengyang, Zhihua Guo, and Huaixin Cao. 2020. "Symmetry-Like Relation of Relative Entropy Measure of Quantum Coherence" Entropy 22, no. 3: 297. https://doi.org/10.3390/e22030297
APA StyleZhang, C., Guo, Z., & Cao, H. (2020). Symmetry-Like Relation of Relative Entropy Measure of Quantum Coherence. Entropy, 22(3), 297. https://doi.org/10.3390/e22030297