Hierarchy of quantum operations in manipulating coherence and entanglement

Hayata Yamasaki1,2,3, Madhav Krishnan Vijayan4, and Min-Hsiu Hsieh4,5

1Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7–3–1 Hongo, Bunkyo-ku, Tokyo 113–8656, Japan
2Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
3Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Vienna, Austria
4Centre for Quantum Software & Information (UTS:QSI), University of Technology Sydney, Sydney NSW, Australia
5Hon Hai Quantum Computing Research Center, Taipei City, Taiwan

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Quantum resource theory under different classes of quantum operations advances multiperspective understandings of inherent quantum-mechanical properties, such as quantum coherence and quantum entanglement. We establish hierarchies of different operations for manipulating coherence and entanglement in distributed settings, where at least one of the two spatially separated parties are restricted from generating coherence. In these settings, we introduce new classes of operations and also characterize those maximal, $i.e.$, the resource-non-generating operations, progressing beyond existing studies on incoherent versions of local operations and classical communication and those of separable operations. The maximal operations admit a semidefinite-programming formulation useful for numerical algorithms, whereas the existing operations not. To establish the hierarchies, we prove a sequence of inclusion relations among the operations by clarifying tasks where separation of the operations appears. We also demonstrate an asymptotically non-surviving separation of the operations in the hierarchy in terms of performance of the task of assisted coherence distillation, where a separation in a one-shot scenario vanishes in the asymptotic limit. Our results serve as fundamental analytical and numerical tools to investigate interplay between coherence and entanglement under different operations in the resource theory.

► BibTeX data

► References

[1] Anurag Anshu, Min-Hsiu Hsieh, and Rahul Jain. Quantifying resources in general resource theory with catalysts. Phys. Rev. Lett., 121: 190504, Nov 2018a. 10.1103/​PhysRevLett.121.190504. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.121.190504.

[2] Anurag Anshu, Rahul Jain, and Alexander Streltsov. Quantum state redistribution with local coherence. arXiv:1804.04915, Apr 2018b. URL https:/​/​arxiv.org/​abs/​1804.04915.

[3] S. Bandyopadhyay, A. Cosentino, N. Johnston, V. Russo, J. Watrous, and N. Yu. Limitations on separable measurements by convex optimization. IEEE Transactions on Information Theory, 61 (6): 3593–3604, June 2015. 10.1109/​TIT.2015.2417755. URL https:/​/​ieeexplore.ieee.org/​document/​7086052.

[4] T. Baumgratz, M. Cramer, and M. B. Plenio. Quantifying coherence. Phys. Rev. Lett., 113: 140401, Sep 2014. 10.1103/​PhysRevLett.113.140401. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.113.140401.

[5] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels. Phys. Rev. Lett., 70 (13): 1895–1899, Mar 1993. 10.1103/​PhysRevLett.70.1895. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.70.1895.

[6] Charles H. Bennett, David P. DiVincenzo, Christopher A. Fuchs, Tal Mor, Eric Rains, Peter W. Shor, John A. Smolin, and William K. Wootters. Quantum nonlocality without entanglement. Phys. Rev. A, 59: 1070–1091, Feb 1999. 10.1103/​PhysRevA.59.1070. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.59.1070.

[7] Tanmoy Biswas, María García Díaz, and Andreas Winter. Interferometric visibility and coherence. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473 (2203): 20170170, 2017. 10.1098/​rspa.2017.0170. URL https:/​/​royalsocietypublishing.org/​doi/​abs/​10.1098/​rspa.2017.0170.

[8] F. G. S. L. Brandao and N. Datta. One-shot rates for entanglement manipulation under non-entangling maps. IEEE Transactions on Information Theory, 57 (3): 1754–1760, March 2011. 10.1109/​TIT.2011.2104531. URL https:/​/​ieeexplore.ieee.org/​abstract/​document/​5714245.

[9] Dipayan Chakraborty, Prabir Kumar Dey, Nabendu Das, Indrani Chattopadhyay, Amit Bhar, and Debasis Sarkar. Necessary and sufficient condition for the equivalence of two pure multipartite states under stochastic local incoherent operations and classical communications. Phys. Rev. A, 100: 052316, Nov 2019. 10.1103/​PhysRevA.100.052316. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.100.052316.

[10] E. Chitambar, A. Streltsov, S. Rana, M. N. Bera, G. Adesso, and M. Lewenstein. Assisted distillation of quantum coherence. Phys. Rev. Lett., 116: 070402, Feb 2016. 10.1103/​PhysRevLett.116.070402. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.116.070402.

[11] Eric Chitambar. Dephasing-covariant operations enable asymptotic reversibility of quantum resources. Phys. Rev. A, 97: 050301, May 2018. 10.1103/​PhysRevA.97.050301. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.97.050301.

[12] Eric Chitambar and Gilad Gour. Comparison of incoherent operations and measures of coherence. Phys. Rev. A, 94: 052336, Nov 2016a. 10.1103/​PhysRevA.94.052336. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.94.052336.

[13] Eric Chitambar and Gilad Gour. Critical examination of incoherent operations and a physically consistent resource theory of quantum coherence. Phys. Rev. Lett., 117: 030401, Jul 2016b. 10.1103/​PhysRevLett.117.030401. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.117.030401.

[14] Eric Chitambar and Gilad Gour. Quantum resource theories. Rev. Mod. Phys., 91: 025001, Apr 2019. 10.1103/​RevModPhys.91.025001. URL https:/​/​link.aps.org/​doi/​10.1103/​RevModPhys.91.025001.

[15] Eric Chitambar and Min-Hsiu Hsieh. Asymptotic state discrimination and a strict hierarchy in distinguishability norms. Journal of Mathematical Physics, 55 (11): 112204, 2014. 10.1063/​1.4902027. URL http:/​/​scitation.aip.org/​content/​aip/​journal/​jmp/​55/​11/​10.1063/​1.4902027.

[16] Eric Chitambar and Min-Hsiu Hsieh. Relating the resource theories of entanglement and quantum coherence. Phys. Rev. Lett., 117: 020402, Jul 2016. 10.1103/​PhysRevLett.117.020402. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.117.020402.

[17] Eric Chitambar and Min-Hsiu Hsieh. Round complexity in the local transformations of quantum and classical states. Nature communications, 8 (1): 2086, 2017. 10.1038/​s41467-017-01887-5. URL https:/​/​www.nature.com/​articles/​s41467-017-01887-5.

[18] Eric Chitambar, Runyao Duan, and Min-Hsiu Hsieh. When do local operations and classical communication suffice for two-qubit state discrimination? IEEE Transactions on Information Theory, 60 (3): 1549–1561, 2014a. 10.1109/​TIT.2013.2295356. URL https:/​/​ieeexplore.ieee.org/​document/​6687245.

[19] Eric Chitambar, Debbie Leung, Laura Mančinska, Maris Ozols, and Andreas Winter. Everything you always wanted to know about locc (but were afraid to ask). Communications in Mathematical Physics, 328 (1): 303–326, May 2014b. 10.1007/​s00220-014-1953-9. URL https:/​/​link.springer.com/​article/​10.1007/​s00220-014-1953-9.

[20] Eric Chitambar, Julio I. de Vicente, Mark W. Girard, and Gilad Gour. Entanglement manipulation beyond local operations and classical communication. Journal of Mathematical Physics, 61 (4): 042201, 2020. 10.1063/​1.5124109. URL https:/​/​aip.scitation.org/​doi/​10.1063/​1.5124109.

[21] J. P. R. Christensen and J. Vesterstrøm. A note on extreme positive definite matrices. Mathematische Annalen, 244 (1): 65–68, Feb 1979. 10.1007/​BF01420337. URL https:/​/​link.springer.com/​article/​10.1007.

[22] Alessandro Cosentino. Positive-partial-transpose-indistinguishable states via semidefinite programming. Phys. Rev. A, 87: 012321, Jan 2013. 10.1103/​PhysRevA.87.012321. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.87.012321.

[23] Matthew J. Donald, Michał Horodecki, and Oliver Rudolph. The uniqueness theorem for entanglement measures. Journal of Mathematical Physics, 43 (9): 4252–4272, 2002. 10.1063/​1.1495917. URL https:/​/​aip.scitation.org/​doi/​abs/​10.1063/​1.1495917.

[24] Dario Egloff, Juan M. Matera, Thomas Theurer, and Martin B. Plenio. Of local operations and physical wires. Phys. Rev. X, 8: 031005, Jul 2018. 10.1103/​PhysRevX.8.031005. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevX.8.031005.

[25] Christopher Eltschka and Jens Siewert. Quantifying entanglement resources. J. Phys. A, 47 (42): 424005, Oct 2014. 10.1088/​1751-8113/​47/​42/​424005. URL http:/​/​iopscience.iop.org/​article/​10.1088/​1751-8113/​47/​42/​424005.

[26] K. Fang, X. Wang, M. Tomamichel, and R. Duan. Non-asymptotic entanglement distillation. IEEE Transactions on Information Theory, 65 (10): 6454–6465, Oct 2019. 10.1109/​TIT.2019.2914688. URL https:/​/​ieeexplore.ieee.org/​document/​8707001.

[27] John Goold, Marcus Huber, Arnau Riera, Lídia del Rio, and Paul Skrzypczyk. The role of quantum information in thermodynamics—a topical review. Journal of Physics A: Mathematical and Theoretical, 49 (14): 143001, feb 2016. 10.1088/​1751-8113/​49/​14/​143001. URL https:/​/​iopscience.iop.org/​article/​10.1088/​1751-8113/​49/​14/​143001.

[28] Aram W. Harrow and Ashley Montanaro. Quantum computational supremacy. Nature, 549: 203–209, Sep 2017. 10.1038/​nature23458. URL https:/​/​www.nature.com/​articles/​nature23458.

[29] Michał Horodecki, Jonathan Oppenheim, and Andreas Winter. Partial quantum information. Nature, 436 (7051): 673–676, Aug 2005. 10.1038/​nature03909. URL http:/​/​www.nature.com/​doifinder/​10.1038/​nature03909.

[30] Michał Horodecki, Jonathan Oppenheim, and Andreas Winter. Quantum state merging and negative information. Comm. Math. Phys., 269 (1): 107–136, Nov 2006. 10.1007/​s00220-006-0118-x. URL http:/​/​link.springer.com/​10.1007/​s00220-006-0118-x.

[31] Pawel Horodecki. Separability criterion and inseparable mixed states with positive partial transposition. Physics Letters A, 232 (5): 333 – 339, 1997. 10.1016/​S0375-9601(97)00416-7. URL http:/​/​www.sciencedirect.com/​science/​article/​pii/​S0375960197004167.

[32] Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki. Quantum entanglement. Rev. Mod. Phys., 81: 865–942, Jun 2009. 10.1103/​RevModPhys.81.865. URL https:/​/​link.aps.org/​doi/​10.1103/​RevModPhys.81.865.

[33] S. F. Huelga and M. B. Plenio. Vibrations, quanta and biology. Contemporary Physics, 54 (4): 181–207, 2013. 10.1080/​00405000.2013.829687. URL https:/​/​www.tandfonline.com/​doi/​abs/​10.1080/​00405000.2013.829687.

[34] Kohdai Kuroiwa and Hayata Yamasaki. General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures. Quantum, 4: 355, November 2020. 10.22331/​q-2020-11-01-355. URL https:/​/​quantum-journal.org/​papers/​q-2020-11-01-355/​.

[35] Kohdai Kuroiwa and Hayata Yamasaki. Consistent measures of general quantum resources: Discord, non-markovianity, and non-gaussianity. arXiv:2103.05665, Mar 2021. URL https:/​/​arxiv.org/​abs/​2103.05665.

[36] Ludovico Lami. Completing the grand tour of asymptotic quantum coherence manipulation. IEEE Transactions on Information Theory, 66 (4): 2165–2183, 2020. 10.1109/​TIT.2019.2945798. URL https:/​/​ieeexplore.ieee.org/​document/​8863412.

[37] Ludovico Lami, Ryuji Takagi, and Gerardo Adesso. Assisted concentration of gaussian resources. Phys. Rev. A, 101: 052305, May 2020. 10.1103/​PhysRevA.101.052305. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.101.052305.

[38] J. Löfberg. Yalmip : a toolbox for modeling and optimization in matlab. In 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), pages 284–289, Taipei, Taiwan, 2004. 10.1109/​CACSD.2004.1393890. URL https:/​/​ieeexplore.ieee.org/​document/​1393890. https:/​/​yalmip.github.io/​.

[39] Yu Luo, Yongming Li, and Min-Hsiu Hsieh. Inequivalent multipartite coherence classes and two operational coherence monotones. Phys. Rev. A, 99: 042306, Apr 2019. 10.1103/​PhysRevA.99.042306. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.99.042306.

[40] Jiajun Ma, Benjamin Yadin, Davide Girolami, Vlatko Vedral, and Mile Gu. Converting coherence to quantum correlations. Phys. Rev. Lett., 116: 160407, Apr 2016. 10.1103/​PhysRevLett.116.160407. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.116.160407.

[41] J M Matera, D Egloff, N Killoran, and M B Plenio. Coherent control of quantum systems as a resource theory. Quantum Science and Technology, 1 (1): 01LT01, aug 2016. 10.1088/​2058-9565/​1/​1/​01lt01. URL https:/​/​iopscience.iop.org/​article/​10.1088/​2058-9565/​1/​1/​01LT01.

[42] Kavan Modi, Aharon Brodutch, Hugo Cable, Tomasz Paterek, and Vlatko Vedral. The classical-quantum boundary for correlations: Discord and related measures. Rev. Mod. Phys., 84: 1655–1707, Nov 2012. 10.1103/​RevModPhys.84.1655. URL https:/​/​link.aps.org/​doi/​10.1103/​RevModPhys.84.1655.

[43] Benjamin Morris, Ludovico Lami, and Gerardo Adesso. Assisted work distillation. Phys. Rev. Lett., 122: 130601, Apr 2019. 10.1103/​PhysRevLett.122.130601. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.122.130601.

[44] B. O'Donoghue, E. Chu, N. Parikh, and S. Boyd. Conic optimization via operator splitting and homogeneous self-dual embedding. Journal of Optimization Theory and Applications, 169 (3): 1042–1068, June 2016. 10.1007/​s10957-016-0892-3. URL https:/​/​link.springer.com/​article/​10.1007/​s10957-016-0892-3. https:/​/​github.com/​cvxgrp/​scs.

[45] S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden. Advances in quantum cryptography. Adv. Opt. Photon., 12 (4): 1012–1236, Dec 2020. 10.1364/​AOP.361502. URL http:/​/​aop.osa.org/​abstract.cfm?URI=aop-12-4-1012.

[46] Martin B. Plbnio and Shashank Virmani. An introduction to entanglement measures. Quantum Inf. Comput., 7 (1): 1–51, Jan 2007. 10.26421/​QIC7.1-2-1. URL http:/​/​www.rintonpress.com/​journals/​doi/​QIC7.1-2-1.html.

[47] Johan Åberg. Subspace preservation, subspace locality, and gluing of completely positive maps. Annals of Physics, 313 (2): 326 – 367, 2004. 10.1016/​j.aop.2004.04.013. URL http:/​/​www.sciencedirect.com/​science/​article/​pii/​S0003491604000879.

[48] Johan Åberg. Quantifying superposition. arXiv:quant-ph/​0612146, Dec 2006. URL https:/​/​arxiv.org/​abs/​quant-ph/​0612146.

[49] Eric M. Rains. Entanglement purification via separable superoperators. arXiv:quant-ph/​9707002, Jul 1997. URL https:/​/​arxiv.org/​abs/​quant-ph/​9707002.

[50] Eric M. Rains. A semidefinite program for distillable entanglement. IEEE Transactions on Information Theory, 47 (7): 2921–2933, Nov 2001. 10.1109/​18.959270. URL https:/​/​ieeexplore.ieee.org/​abstract/​document/​959270.

[51] Bartosz Regula, Kun Fang, Xin Wang, and Gerardo Adesso. One-shot coherence distillation. Phys. Rev. Lett., 121: 010401, Jul 2018a. 10.1103/​PhysRevLett.121.010401. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.121.010401.

[52] Bartosz Regula, Ludovico Lami, and Alexander Streltsov. Nonasymptotic assisted distillation of quantum coherence. Phys. Rev. A, 98: 052329, Nov 2018b. 10.1103/​PhysRevA.98.052329. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.98.052329.

[53] Bartosz Regula, Kun Fang, Xin Wang, and Mile Gu. One-shot entanglement distillation beyond local operations and classical communication. New Journal of Physics, 21 (10): 103017, oct 2019. 10.1088/​1367-2630/​ab4732. URL https:/​/​iopscience.iop.org/​article/​10.1088/​1367-2630/​ab4732.

[54] John A. Smolin, Frank Verstraete, and Andreas Winter. Entanglement of assistance and multipartite state distillation. Phys. Rev. A, 72: 052317, Nov 2005. 10.1103/​PhysRevA.72.052317. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.72.052317.

[55] A. Streltsov, E. Chitambar, S. Rana, M. N. Bera, A. Winter, and M. Lewenstein. Entanglement and coherence in quantum state merging. Phys. Rev. Lett., 116: 240405, Jun 2016. 10.1103/​PhysRevLett.116.240405. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.116.240405.

[56] Alexander Streltsov, Gerardo Adesso, and Martin B. Plenio. Colloquium: Quantum coherence as a resource. Rev. Mod. Phys., 89: 041003, Oct 2017a. 10.1103/​RevModPhys.89.041003. URL https:/​/​link.aps.org/​doi/​10.1103/​RevModPhys.89.041003.

[57] Alexander Streltsov, Swapan Rana, Manabendra Nath Bera, and Maciej Lewenstein. Towards resource theory of coherence in distributed scenarios. Phys. Rev. X, 7: 011024, Mar 2017b. 10.1103/​PhysRevX.7.011024. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevX.7.011024.

[58] V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight. Quantifying entanglement. Phys. Rev. Lett., 78: 2275–2279, Mar 1997. 10.1103/​PhysRevLett.78.2275. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.78.2275.

[59] Madhav Krishnan Vijayan, Eric Chitambar, and Min-Hsiu Hsieh. One-shot assisted concentration of coherence. Journal of Physics A: Mathematical and Theoretical, 51 (41): 414001, Sep 2018. 10.1088/​1751-8121/​aadc21. URL https:/​/​iopscience.iop.org/​article/​10.1088/​1751-8121/​aadc21.

[60] Xin Wang and Runyao Duan. Improved semidefinite programming upper bound on distillable entanglement. Phys. Rev. A, 94: 050301, Nov 2016. 10.1103/​PhysRevA.94.050301. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.94.050301.

[61] Xin Wang and Runyao Duan. Irreversibility of asymptotic entanglement manipulation under quantum operations completely preserving positivity of partial transpose. Phys. Rev. Lett., 119: 180506, Nov 2017. 10.1103/​PhysRevLett.119.180506. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.119.180506.

[62] Xin Wang and Mark M. Wilde. Exact entanglement cost of quantum states and channels under ppt-preserving operations. arXiv:1809.09592, Sep 2018. URL https:/​/​arxiv.org/​abs/​1809.09592.

[63] Xin Wang and Mark M. Wilde. Cost of quantum entanglement simplified. Phys. Rev. Lett., 125: 040502, Jul 2020. 10.1103/​PhysRevLett.125.040502. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.125.040502.

[64] John Watrous. Quantum Computational Complexity, pages 7174–7201. Springer New York, New York, NY, 2009. ISBN 978-0-387-30440-3. 10.1007/​978-0-387-30440-3_428. URL https:/​/​link.springer.com/​referenceworkentry/​10.1007%2F978-0-387-30440-3_428.

[65] John Watrous. The Theory of Quantum Information. Cambridge University Press, New York, NY, USA, 1st edition, 2018. ISBN 1107180562, 9781107180567. 10.1017/​9781316848142. URL https:/​/​cs.uwaterloo.ca/​ watrous/​TQI/​.

[66] Stephanie Wehner, David Elkouss, and Ronald Hanson. Quantum internet: A vision for the road ahead. Science, 362 (6412), 2018. 10.1126/​science.aam9288. URL https:/​/​science.sciencemag.org/​content/​362/​6412/​eaam9288.

[67] Andreas Winter and Dong Yang. Operational resource theory of coherence. Phys. Rev. Lett., 116: 120404, Mar 2016. 10.1103/​PhysRevLett.116.120404. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.116.120404.

[68] Kang-Da Wu, Zhibo Hou, Han-Sen Zhong, Yuan Yuan, Guo-Yong Xiang, Chuan-Feng Li, and Guang-Can Guo. Experimentally obtaining maximal coherence via assisted distillation process. Optica, 4 (4): 454–459, Apr 2017. 10.1364/​OPTICA.4.000454. URL http:/​/​www.osapublishing.org/​optica/​abstract.cfm?URI=optica-4-4-454.

[69] Kang-Da Wu, Zhibo Hou, Yuan-Yuan Zhao, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo, Jiajun Ma, Qiong-Yi He, Jayne Thompson, and Mile Gu. Experimental cyclic interconversion between coherence and quantum correlations. Phys. Rev. Lett., 121: 050401, Aug 2018. 10.1103/​PhysRevLett.121.050401. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.121.050401.

[70] Kang-Da Wu, Thomas Theurer, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo, Martin B. Plenio, and Alexander Streltsov. Quantum coherence and state conversion: theory and experiment. npj Quantum Information, 6: 22, Feb 2020. 10.1038/​s41534-020-0250-z. URL https:/​/​www.nature.com/​articles/​s41534-020-0250-z.

[71] Benjamin Yadin, Jiajun Ma, Davide Girolami, Mile Gu, and Vlatko Vedral. Quantum processes which do not use coherence. Phys. Rev. X, 6: 041028, Nov 2016. 10.1103/​PhysRevX.6.041028. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevX.6.041028.

[72] H. Yamasaki and M. Murao. Quantum state merging for arbitrarily small-dimensional systems. IEEE Transactions on Information Theory, 65 (6): 3950–3972, June 2019. 10.1109/​TIT.2018.2889829. URL https:/​/​ieeexplore.ieee.org/​document/​8590809.

[73] Hayata Yamasaki. Entanglement theory in distributed quantum information processing. PhD thesis, The University of Tokyo, 2019. URL https:/​/​arxiv.org/​abs/​1903.09655.

[74] Hayata Yamasaki and Mio Murao. Spread quantum information in one-shot quantum state merging. arXiv:1903.03619, Mar 2019a. URL https:/​/​arxiv.org/​abs/​1903.03619.

[75] Hayata Yamasaki and Mio Murao. Distributed encoding and decoding of quantum information over networks. Advanced Quantum Technologies, 2 (1-2): 1800066, 2019b. 10.1002/​qute.201800066. URL https:/​/​onlinelibrary.wiley.com/​doi/​abs/​10.1002/​qute.201800066. and references therein.

[76] Hayata Yamasaki, Akihito Soeda, and Mio Murao. Graph-associated entanglement cost of a multipartite state in exact and finite-block-length approximate constructions. Phys. Rev. A, 96: 032330, Sep 2017. 10.1103/​PhysRevA.96.032330. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.96.032330.

[77] N. Yu, R. Duan, and M. Ying. Distinguishability of quantum states by positive operator-valued measures with positive partial transpose. IEEE Transactions on Information Theory, 60 (4): 2069–2079, April 2014. 10.1109/​TIT.2014.2307575. URL https:/​/​ieeexplore.ieee.org/​document/​6747300.

[78] Nengkun Yu, Runyao Duan, and Mingsheng Ying. Four locally indistinguishable ququad-ququad orthogonal maximally entangled states. Phys. Rev. Lett., 109: 020506, Jul 2012. 10.1103/​PhysRevLett.109.020506. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.109.020506.

[79] Qi Zhao, Yunchao Liu, Xiao Yuan, Eric Chitambar, and Xiongfeng Ma. One-shot coherence dilution. Phys. Rev. Lett., 120: 070403, Feb 2018. 10.1103/​PhysRevLett.120.070403. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.120.070403.

Cited by

[1] Shuyi Zhang, Yu Luo, Lian-He Shao, Zhengjun Xi, and Heng Fan, "One-shot assisted distillation of coherence via one-way local quantum-incoherent operations and classical communication", Physical Review A 102 5, 052405 (2020).

[2] Masahito Hayashi, Kun Fang, and Kun Wang, "Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction", arXiv:2002.12004.

The above citations are from SAO/NASA ADS (last updated successfully 2021-08-04 06:45:42). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2021-08-04 06:45:40).