Resonant Multilevel Amplitude Damping Channels

Stefano Chessa1,2 and Vittorio Giovannetti1

1NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
2Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois, 61801, USA

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Abstract

We introduce a new set of quantum channels: resonant multilevel amplitude damping (ReMAD) channels. Among other instances, they can describe energy dissipation effects in multilevel atomic systems induced by the interaction with a zero-temperature bosonic environment. At variance with the already known class of multilevel amplitude damping (MAD) channels, this new class of maps allows the presence of an environment unable to discriminate transitions with identical energy gaps. After characterizing the algebra of their composition rules, by analyzing the qutrit case, we show that this new set of channels can exhibit degradability and antidegradability in vast regions of the allowed parameter space. There we compute their quantum capacity and private classical capacity. We show that these capacities can be computed exactly also in regions of the parameter space where the channels aren't degradable nor antidegradable.

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► References

[1] D. Cozzolino, B. Da Lio, D. Bacco, and L. K. Oxenløwe, Advanced Quantum Technologies 2, 1900038 (2019), URL https:/​/​doi.org/​10.1002/​qute.201900038.
https:/​/​doi.org/​10.1002/​qute.201900038

[2] Y. Wang, Z. Hu, B. C. Sanders, and S. Kais, Frontiers in Physics 8, 479 (2020), ISSN 2296-424X, URL https:/​/​doi.org/​10.3389/​fphy.2020.589504.
https:/​/​doi.org/​10.3389/​fphy.2020.589504

[3] A. Hill, Beyond qubits: Unlocking the third state in quantum processors (2021), URL https:/​/​medium.com/​rigetti/​beyond-qubits-unlocking-the-third-state-in-quantum-processors-12d2f84133c4.
https:/​/​medium.com/​rigetti/​beyond-qubits-unlocking-the-third-state-in-quantum-processors-12d2f84133c4

[4] M. Fanizza, F. Kianvash, and V. Giovannetti, Phys. Rev. Lett. 125, 020503 (2020), URL https:/​/​doi.org/​10.1103/​PhysRevLett.125.020503.
https:/​/​doi.org/​10.1103/​PhysRevLett.125.020503

[5] F. Kianvash, M. Fanizza, and V. Giovannetti, Quantum 6, 647 (2022), ISSN 2521-327X, URL https:/​/​doi.org/​10.22331/​q-2022-02-09-647.
https:/​/​doi.org/​10.22331/​q-2022-02-09-647

[6] I. Devetak and P. W. Shor, Communications in Mathematical Physics 256, 287 (2005), URL https:/​/​doi.org/​10.1007/​s00220-005-1317-6.
https:/​/​doi.org/​10.1007/​s00220-005-1317-6

[7] A. D'Arrigo, G. Benenti, and G. Falci, New Journal of Physics 9, 310 (2007), URL https:/​/​doi.org/​10.1088/​1367-2630/​9/​9/​310.
https:/​/​doi.org/​10.1088/​1367-2630/​9/​9/​310

[8] S. Chessa and V. Giovannetti, Communications Physics 4, 22 (2021a), ISSN 2399-3650, URL https:/​/​doi.org/​10.1038/​s42005-021-00524-4.
https:/​/​doi.org/​10.1038/​s42005-021-00524-4

[9] S. Chessa and V. Giovannetti, Quantum 5, 504 (2021b), ISSN 2521-327X, URL https:/​/​doi.org/​10.22331/​q-2021-07-15-504.
https:/​/​doi.org/​10.22331/​q-2021-07-15-504

[10] F. Leditzky, D. Leung, V. Siddhu, G. Smith, and J. Smolin, The platypus of the quantum channel zoo (2022), arXiv:2202.08380, URL https:/​/​doi.org/​10.48550/​arXiv.2202.08380.
https:/​/​doi.org/​10.48550/​arXiv.2202.08380
arXiv:2202.08380

[11] T. S. Cubitt, M. B. Ruskai, and G. Smith, Journal of Mathematical Physics 49, 102104 (2008), URL https:/​/​doi.org/​10.1063/​1.2953685.
https:/​/​doi.org/​10.1063/​1.2953685

[12] S. Singh and N. Datta, npj Quantum Information 8, 50 (2022), ISSN 2056-6387, URL https:/​/​doi.org/​10.1038/​s41534-022-00550-2.
https:/​/​doi.org/​10.1038/​s41534-022-00550-2

[13] A. S. Holevo, Quantum Systems, Channels, Information (De Gruyter, 2019), URL https:/​/​doi.org/​10.1515/​9783110642490.
https:/​/​doi.org/​10.1515/​9783110642490

[14] M. M. Wilde, Quantum Information Theory (Cambridge University Press, Cambridge, 2017), 2nd ed., ISBN 9781107176164, URL https:/​/​doi.org/​10.1017/​9781316809976.
https:/​/​doi.org/​10.1017/​9781316809976

[15] J. Watrous, The Theory of Quantum Information (Cambridge University Press, Cambridge, 2018), ISBN 9781107180567, URL https:/​/​doi.org/​10.1017/​9781316848142.
https:/​/​doi.org/​10.1017/​9781316848142

[16] M. Hayashi, Quantum information theory (Springer, 2017), 2nd ed., ISBN 9783662497234, URL https:/​/​doi.org/​10.1007/​978-3-662-49725-8.
https:/​/​doi.org/​10.1007/​978-3-662-49725-8

[17] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, Cambridge, 2010), ISBN 9781107002173, URL https:/​/​doi.org/​10.1017/​CBO9780511976667.
https:/​/​doi.org/​10.1017/​CBO9780511976667

[18] S. Imre and L. Gyongyosi, Advanced Quantum Communications: An Engineering Approach (Wiley-IEEE Press, 2012), 1st ed., ISBN 1118002369, URL https:/​/​doi.org/​10.1002/​9781118337462.
https:/​/​doi.org/​10.1002/​9781118337462

[19] A. S. Holevo and V. Giovannetti, Reports on Progress in Physics 75, 046001 (2012), URL https:/​/​doi.org/​10.1088/​0034-4885/​75/​4/​046001.
https:/​/​doi.org/​10.1088/​0034-4885/​75/​4/​046001

[20] L. Gyongyosi, S. Imre, and H. V. Nguyen, IEEE Communications Surveys Tutorials 20, 1149 (2018), URL https:/​/​doi.org/​10.1109/​COMST.2017.2786748.
https:/​/​doi.org/​10.1109/​COMST.2017.2786748

[21] Y. Huang, New Journal of Physics 16, 033027 (2014), URL https:/​/​doi.org/​10.1088/​1367-2630/​16/​3/​033027.
https:/​/​doi.org/​10.1088/​1367-2630/​16/​3/​033027

[22] T. Cubitt, D. Elkouss, W. Matthews, M. Ozols, D. Pérez-García, and S. Strelchuk, Nature Communications 6, 6739 (2015), ISSN 2041-1723, URL https:/​/​doi.org/​10.1038/​ncomms7739.
https:/​/​doi.org/​10.1038/​ncomms7739

[23] D. Elkouss and D. Pérez-García, Nature Communications 9, 1149 (2018), ISSN 2041-1723, URL https:/​/​doi.org/​10.1038/​s41467-018-03428-0.
https:/​/​doi.org/​10.1038/​s41467-018-03428-0

[24] M. B. Hastings, Nature Physics 5, 255 (2009), ISSN 1745-2481, URL https:/​/​doi.org/​10.1038/​nphys1224.
https:/​/​doi.org/​10.1038/​nphys1224

[25] G. Smith and J. Yard, Science 321, 1812 (2008), URL https:/​/​doi.org/​10.1126/​science.1162242.
https:/​/​doi.org/​10.1126/​science.1162242

[26] K. Li, A. Winter, X. Zou, and G. Guo, Phys. Rev. Lett. 103, 120501 (2009), URL https:/​/​doi.org/​10.1103/​PhysRevLett.103.120501.
https:/​/​doi.org/​10.1103/​PhysRevLett.103.120501

[27] E. Y. Zhu, Q. Zhuang, M.-H. Hsieh, and P. W. Shor, IEEE Transactions on Information Theory 65, 3973 (2019), URL https:/​/​doi.org/​10.1109/​TIT.2018.2889082.
https:/​/​doi.org/​10.1109/​TIT.2018.2889082

[28] E. Y. Zhu, Q. Zhuang, and P. W. Shor, Phys. Rev. Lett. 119, 040503 (2017), URL https:/​/​doi.org/​10.1103/​PhysRevLett.119.040503.
https:/​/​doi.org/​10.1103/​PhysRevLett.119.040503

[29] F. Caruso and V. Giovannetti, Phys. Rev. A 74, 062307 (2006), URL https:/​/​doi.org/​10.1103/​PhysRevA.74.062307.
https:/​/​doi.org/​10.1103/​PhysRevA.74.062307

[30] G. Smith and J. A. Smolin, in 2008 IEEE Information Theory Workshop (2008), pp. 368–372, URL https:/​/​doi.org/​10.1109/​ITW.2008.4578688.
https:/​/​doi.org/​10.1109/​ITW.2008.4578688

[31] K. Brádler, N. Dutil, P. Hayden, and A. Muhammad, Journal of Mathematical Physics 51, 072201 (2010), URL https:/​/​doi.org/​10.1063/​1.3449555.
https:/​/​doi.org/​10.1063/​1.3449555

[32] S. Watanabe, Phys. Rev. A 85, 012326 (2012), URL https:/​/​doi.org/​10.1103/​PhysRevA.85.012326.
https:/​/​doi.org/​10.1103/​PhysRevA.85.012326

[33] L. Gyongyosi, IEEE Access 2, 333 (2014), URL https:/​/​doi.org/​10.1109/​ACCESS.2014.2317652.
https:/​/​doi.org/​10.1109/​ACCESS.2014.2317652

[34] D. Sutter, V. B. Scholz, A. Winter, and R. Renner, IEEE Transactions on Information Theory 63, 7832 (2017), URL https:/​/​doi.org/​10.1109/​TIT.2017.2754268.
https:/​/​doi.org/​10.1109/​TIT.2017.2754268

[35] S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, Nature Communications 8, 15043 (2017), ISSN 2041-1723, URL https:/​/​doi.org/​10.1038/​ncomms15043.
https:/​/​doi.org/​10.1038/​ncomms15043

[36] A. Anshu, in 2017 IEEE Information Theory Workshop (ITW) (2017), pp. 214–218, URL https:/​/​doi.org/​10.1109/​ITW.2017.8277947.
https:/​/​doi.org/​10.1109/​ITW.2017.8277947

[37] F. Leditzky, D. Leung, and G. Smith, Phys. Rev. Lett. 120, 160503 (2018), URL https:/​/​doi.org/​10.1103/​PhysRevLett.120.160503.
https:/​/​doi.org/​10.1103/​PhysRevLett.120.160503

[38] M. Tomamichel, M. M. Wilde, and A. Winter, IEEE Transactions on Information Theory 63, 715 (2017), URL https:/​/​doi.org/​10.1109/​TIT.2016.2615847.
https:/​/​doi.org/​10.1109/​TIT.2016.2615847

[39] M. M. Wilde, M. Tomamichel, and M. Berta, IEEE Transactions on Information Theory 63, 1792 (2017), URL https:/​/​doi.org/​10.1109/​TIT.2017.2648825.
https:/​/​doi.org/​10.1109/​TIT.2017.2648825

[40] M. Christandl and A. Müller-Hermes, Communications in Mathematical Physics 353, 821 (2017), ISSN 1432-0916, URL https:/​/​doi.org/​10.1007/​s00220-017-2885-y.
https:/​/​doi.org/​10.1007/​s00220-017-2885-y

[41] X. Wang, K. Fang, and R. Duan, IEEE Transactions on Information Theory 65, 2583 (2019), URL https:/​/​doi.org/​10.1109/​TIT.2018.2874031.
https:/​/​doi.org/​10.1109/​TIT.2018.2874031

[42] C. Hirche, C. Rouzé, and D. Stilck França, Quantum 6, 862 (2022), ISSN 2521-327X, URL https:/​/​doi.org/​10.22331/​q-2022-11-28-862.
https:/​/​doi.org/​10.22331/​q-2022-11-28-862

[43] K. Fang and H. Fawzi, Communications in Mathematical Physics 384, 1615 (2021), ISSN 1432-0916, URL https:/​/​doi.org/​10.1007/​s00220-021-04064-4.
https:/​/​doi.org/​10.1007/​s00220-021-04064-4

[44] C. Hirche and F. Leditzky, Bounding quantum capacities via partial orders and complementarity (2022), arXiv:2202.11688, URL https:/​/​doi.org/​10.48550/​arXiv.2202.11688.
https:/​/​doi.org/​10.48550/​arXiv.2202.11688
arXiv:2202.11688

[45] O. Fawzi, A. Shayeghi, and H. Ta, in 2021 IEEE International Symposium on Information Theory (ISIT) (2021), pp. 272–277, URL https:/​/​doi.org/​10.1109/​ISIT45174.2021.9517913.
https:/​/​doi.org/​10.1109/​ISIT45174.2021.9517913

[46] K. Hammerer, A. S. Sørensen, and E. S. Polzik, Rev. Mod. Phys. 82, 1041 (2010), URL https:/​/​doi.org/​10.1103/​RevModPhys.82.1041.
https:/​/​doi.org/​10.1103/​RevModPhys.82.1041

[47] N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, Rev. Mod. Phys. 83, 33 (2011), URL https:/​/​doi.org/​10.1103/​RevModPhys.83.33.
https:/​/​doi.org/​10.1103/​RevModPhys.83.33

[48] A. Reiserer and G. Rempe, Rev. Mod. Phys. 87, 1379 (2015), URL https:/​/​doi.org/​10.1103/​RevModPhys.87.1379.
https:/​/​doi.org/​10.1103/​RevModPhys.87.1379

[49] J. N. Damask, Polarization optics in telecommunications (Springer Series in Optical Sciences, 2005), 1st ed., ISBN 978-0-387-26302-1, URL https:/​/​doi.org/​10.1007/​b137386.
https:/​/​doi.org/​10.1007/​b137386

[50] D. Gottesman, A. Kitaev, and J. Preskill, Phys. Rev. A 64, 012310 (2001), URL https:/​/​doi.org/​10.1103/​PhysRevA.64.012310.
https:/​/​doi.org/​10.1103/​PhysRevA.64.012310

[51] S. D. Bartlett, H. de Guise, and B. C. Sanders, Phys. Rev. A 65, 052316 (2002), URL https:/​/​doi.org/​10.1103/​PhysRevA.65.052316.
https:/​/​doi.org/​10.1103/​PhysRevA.65.052316

[52] B. M. Terhal, J. Conrad, and C. Vuillot, Quantum Science and Technology 5, 043001 (2020), URL https:/​/​doi.org/​10.1088/​2058-9565/​ab98a5.
https:/​/​doi.org/​10.1088/​2058-9565/​ab98a5

[53] W. Cai, Y. Ma, W. Wang, C.-L. Zou, and L. Sun, Fundamental Research 1, 50 (2021), ISSN 2667-3258, URL https:/​/​doi.org/​10.1016/​j.fmre.2020.12.006.
https:/​/​doi.org/​10.1016/​j.fmre.2020.12.006

[54] S. Carretta, D. Zueco, A. Chiesa, Á. Gómez-León, and F. Luis, Applied Physics Letters 118, 240501 (2021), URL https:/​/​doi.org/​10.1063/​5.0053378.
https:/​/​doi.org/​10.1063/​5.0053378

[55] W. F. Stinespring, Proceedings of the American Mathematical Society 6, 211 (1955), URL https:/​/​doi.org/​10.2307/​2032342.
https:/​/​doi.org/​10.2307/​2032342

[56] K. Kraus, Annals of Physics 64, 311 (1971), ISSN 0003-4916, URL https:/​/​doi.org/​10.1016/​0003-4916(71)90108-4.
https:/​/​doi.org/​10.1016/​0003-4916(71)90108-4

[57] Y. Ouyang, Quantum Information and Computation 14, 917 (2014), URL https:/​/​doi.org/​10.26421/​QIC14.11-12-2.
https:/​/​doi.org/​10.26421/​QIC14.11-12-2

[58] O. Fawzi, A. Müller-Hermes, and A. Shayeghi, in 13th Innovations in Theoretical Computer Science Conference (ITCS 2022), edited by M. Braverman (Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2022), vol. 215 of Leibniz International Proceedings in Informatics (LIPIcs), pp. 68:1–68:20, ISBN 978-3-95977-217-4, ISSN 1868-8969, URL https:/​/​doi.org/​10.4230/​LIPIcs.ITCS.2022.68.
https:/​/​doi.org/​10.4230/​LIPIcs.ITCS.2022.68

[59] B. Schumacher and M. A. Nielsen, Phys. Rev. A 54, 2629 (1996), URL https:/​/​doi.org/​10.1103/​PhysRevA.54.2629.
https:/​/​doi.org/​10.1103/​PhysRevA.54.2629

[60] S. Lloyd, Phys. Rev. A 55, 1613 (1997), URL https:/​/​doi.org/​10.1103/​PhysRevA.55.1613.
https:/​/​doi.org/​10.1103/​PhysRevA.55.1613

[61] P. W. Shor, in Lecture notes, MSRI Workshop on Quantum Computation (Quantum Information and Cryptography) (2002), URL https:/​/​www.msri.org/​workshops/​203/​schedules/​1181.
https:/​/​www.msri.org/​workshops/​203/​schedules/​1181

[62] I. Devetak, IEEE Transactions on Information Theory 51, 44 (2005), URL https:/​/​doi.org/​10.1109/​TIT.2004.839515.
https:/​/​doi.org/​10.1109/​TIT.2004.839515

[63] A. S. Holevo, Problemy Peredachi Informatsii 9, 3 (1973), URL http:/​/​www.mathnet.ru/​eng/​ppi903.
http:/​/​www.mathnet.ru/​eng/​ppi903

[64] N. Cai, A. Winter, and R. W. Yeung, Problems of Information Transmission 40, 318 (2004), URL https:/​/​doi.org/​10.1007/​s11122-005-0002-x.
https:/​/​doi.org/​10.1007/​s11122-005-0002-x

[65] M. M. Wolf and D. Perez-Garcia, Physical Review A 75, 012303 (2007), URL https:/​/​doi.org/​10.1103/​PhysRevA.75.012303.
https:/​/​doi.org/​10.1103/​PhysRevA.75.012303

[66] G. Smith and J. A. Smolin, Physical review letters 98, 030501 (2007), URL https:/​/​doi.org/​10.1103/​PhysRevLett.98.030501.
https:/​/​doi.org/​10.1103/​PhysRevLett.98.030501

[67] G. Smith, Physical Review A 78, 022306 (2008), URL https:/​/​doi.org/​10.1103/​PhysRevA.78.022306.
https:/​/​doi.org/​10.1103/​PhysRevA.78.022306

[68] J. Yard, P. Hayden, and I. Devetak, IEEE Transactions on Information Theory 54, 3091 (2008), URL https:/​/​doi.org/​10.1109/​TIT.2008.924665.
https:/​/​doi.org/​10.1109/​TIT.2008.924665

[69] C. H. Bennett, D. P. DiVincenzo, and J. A. Smolin, Phys. Rev. Lett. 78, 3217 (1997), URL https:/​/​doi.org/​10.1103/​PhysRevLett.78.3217.
https:/​/​doi.org/​10.1103/​PhysRevLett.78.3217

[70] V. Giovannetti and R. Fazio, Phys. Rev. A 71, 032314 (2005), URL https:/​/​doi.org/​10.1103/​PhysRevA.71.032314.
https:/​/​doi.org/​10.1103/​PhysRevA.71.032314

[71] K. Brádler, Open Systems & Information Dynamics 22, 1550026 (2015), URL https:/​/​doi.org/​10.1142/​S1230161215500262.
https:/​/​doi.org/​10.1142/​S1230161215500262

[72] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993), URL https:/​/​doi.org/​10.1103/​PhysRevLett.70.1895.
https:/​/​doi.org/​10.1103/​PhysRevLett.70.1895

[73] C. H. Bennett and S. J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992), URL https:/​/​doi.org/​10.1103/​PhysRevLett.69.2881.
https:/​/​doi.org/​10.1103/​PhysRevLett.69.2881

[74] C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal, Phys. Rev. Lett. 83, 3081 (1999), URL https:/​/​doi.org/​10.1103/​PhysRevLett.83.3081.
https:/​/​doi.org/​10.1103/​PhysRevLett.83.3081

[75] C. Bennett, P. Shor, J. Smolin, and A. Thapliyal, IEEE Transactions on Information Theory 48, 2637 (2002), URL https:/​/​doi.org/​10.1109/​TIT.2002.802612.
https:/​/​doi.org/​10.1109/​TIT.2002.802612

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