Smooth Metric Adjusted Skew Information Rates

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Koji Yamaguchi¹ and Hiroyasu Tajima^2,3

¹Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
²Department of Communication Engineering and Informatics, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan
³JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan

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Abstract

Metric adjusted skew information, induced from quantum Fisher information, is a well-known family of resource measures in the resource theory of asymmetry. However, its asymptotic rates are not valid asymmetry monotone since it has an asymptotic discontinuity. We here introduce a new class of asymmetry measures with the smoothing technique, which we term smooth metric adjusted skew information. We prove that its asymptotic sup- and inf-rates are valid asymptotic measures in the resource theory of asymmetry. Furthermore, it is proven that the smooth metric adjusted skew information rates provide a lower bound for the coherence cost and an upper bound for the distillable coherence.

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► BibTeX data

@article{Yamaguchi2023smoothmetric, doi = {10.22331/q-2023-05-22-1012}, url = {https://doi.org/10.22331/q-2023-05-22-1012}, title = {Smooth {M}etric {A}djusted {S}kew {I}nformation {R}ates}, author = {Yamaguchi, Koji and Tajima, Hiroyasu}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1012}, month = may, year = {2023}<br /> }

► References

[1] E. P. Wigner, Zeitschrift für Physik A Hadrons and nuclei 133, 101 (1952).
https://doi.org/10.1007/BF01948686

[2] H. Araki and M. M. Yanase, Physical Review 120, 622 (1960).
https://doi.org/10.1103/PhysRev.120.622

[3] E. P. Wigner and M. M. Yanase, Proceedings of the National Academy of Sciences 49, 910 (1963), publisher: Proceedings of the National Academy of Sciences.
https://doi.org/10.1073/pnas.49.6.910

[4] P. Gibilisco and T. Isola, Infinite Dimensional Analysis, Quantum Probability and Related Topics 04, 553 (2001).
https://doi.org/10.1142/S0219025701000644

[5] P. Gibilisco and T. Isola, Journal of Mathematical Physics 44, 3752 (2003).
https://doi.org/10.1063/1.1598279

[6] F. Hansen, Proceedings of the National Academy of Sciences 105, 9909 (2008).
https://doi.org/10.1073/pnas.0803323105

[7] E. Chitambar and G. Gour, Reviews of Modern Physics 91, 025001 (2019).
https://doi.org/10.1103/RevModPhys.91.025001

[8] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Reviews of Modern Physics 81, 865 (2009).
https://doi.org/10.1103/RevModPhys.81.865

[9] J. Aberg, arXiv:quant-ph/0612146 (2006).
https://doi.org/10.48550/arXiv.quant-ph/0612146
arXiv:quant-ph/0612146

[10] T. Baumgratz, M. Cramer, and M. Plenio, Physical Review Letters 113, 140401 (2014).
https://doi.org/10.1103/PhysRevLett.113.140401

[11] A. Streltsov, G. Adesso, and M. B. Plenio, Reviews of Modern Physics 89, 041003 (2017).
https://doi.org/10.1103/RevModPhys.89.041003

[12] F. G. S. L. Brandão, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, Physical Review Letters 111, 250404 (2013).
https://doi.org/10.1103/PhysRevLett.111.250404

[13] F. Brandão, M. Horodecki, N. Ng, J. Oppenheim, and S. Wehner, Proceedings of the National Academy of Sciences 112, 3275 (2015).
https://doi.org/10.1073/pnas.1411728112

[14] G. Gour and R. W. Spekkens, New Journal of Physics 10, 033023 (2008).
https://doi.org/10.1088/1367-2630/10/3/033023

[15] I. Marvian and R. W. Spekkens, Nature Communications 5, 3821 (2014).
https://doi.org/10.1038/ncomms4821

[16] V. Giovannetti, S. Lloyd, and L. Maccone, Nature 412, 417 (2001).
https://doi.org/10.1038/35086525

[17] V. Giovannetti, S. Lloyd, and L. Maccone, Physical Review Letters 96, 010401 (2006).
https://doi.org/10.1103/PhysRevLett.96.010401

[18] F. Giacomini, E. Castro-Ruiz, and Č. Brukner, Nature Communications 10, 494 (2019).
https://doi.org/10.1038/s41467-018-08155-0

[19] R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, Nature Communications 1, 121 (2010).
https://doi.org/10.1038/ncomms1122

[20] I. Marvian, Nature Communications 11, 25 (2020).
https://doi.org/10.1038/s41467-019-13846-3

[21] M. P. Woods, R. Silva, and J. Oppenheim, Annales Henri Poincaré 20, 125 (2019).
https://doi.org/10.1007/s00023-018-0736-9

[22] I. Marvian, R. W. Spekkens, and P. Zanardi, Physical Review A 93, 052331 (2016).
https://doi.org/10.1103/PhysRevA.93.052331

[23] M. Lostaglio, D. Jennings, and T. Rudolph, Nature Communications 6, 6383 (2015).
https://doi.org/10.1038/ncomms7383

[24] M. M. Yanase, Physical Review 123, 666 (1961).
https://doi.org/10.1103/PhysRev.123.666

[25] M. Ozawa, Physical Review Letters 88, 050402 (2002a).
https://doi.org/10.1103/PhysRevLett.88.050402

[26] K. Korzekwa, Resource theory of asymmetry, Ph.D. thesis, Imperial College London (2003).

[27] H. Tajima and H. Nagaoka, arXiv:1909.02904 [cond-mat, physics:quant-ph] (2019).
https://doi.org/10.48550/arXiv.1909.02904
arXiv:1909.02904

[28] Y. Kuramochi and H. Tajima, “Wigner-Araki-Yanase theorem for continuous and unbounded conserved observables,” (2022).
https://doi.org/10.48550/arXiv.2208.13494

[29] M. Ozawa, Physical Review Letters 89, 057902 (2002b).
https://doi.org/10.1103/PhysRevLett.89.057902

[30] H. Tajima, N. Shiraishi, and K. Saito, Physical Review Letters 121, 110403 (2018).
https://doi.org/10.1103/PhysRevLett.121.110403

[31] H. Tajima, N. Shiraishi, and K. Saito, Physical Review Research 2, 043374 (2020).
https://doi.org/10.1103/PhysRevResearch.2.043374

[32] H. Tajima and K. Saito, arXiv:2103.01876 [cond-mat, physics:quant-ph] (2021).
https://doi.org/10.48550/arXiv.2103.01876
arXiv:2103.01876

[33] H. Tajima, R. Takagi, and Y. Kuramochi, “Universal trade-off structure between symmetry, irreversibility, and quantum coherence in quantum processes,” (2022).
https://doi.org/10.48550/arXiv.2206.11086

[34] A. Kubica and R. Demkowicz-Dobrzański, Physical Review Letters 126, 150503 (2021).
https://doi.org/10.1103/PhysRevLett.126.150503

[35] S. Zhou, Z.-W. Liu, and L. Jiang, Quantum 5, 521 (2021).
https://doi.org/10.22331/q-2021-08-09-521

[36] Y. Yang, Y. Mo, J. M. Renes, G. Chiribella, and M. P. Woods, Physical Review Research 4, 023107 (2022).
https://doi.org/10.1103/PhysRevResearch.4.023107

[37] Z.-W. Liu and S. Zhou, arXiv:2111.06360 [quant-ph] (2022).
https://doi.org/10.48550/arXiv.2111.06360
arXiv:2111.06360

[38] C. Zhang, B. Yadin, Z.-B. Hou, H. Cao, B.-H. Liu, Y.-F. Huang, R. Maity, V. Vedral, C.-F. Li, G.-C. Guo, and D. Girolami, Physical Review A 96, 042327 (2017).
https://doi.org/10.1103/PhysRevA.96.042327

[39] R. Takagi, Scientific Reports 9, 14562 (2019).
https://doi.org/10.1038/s41598-019-50279-w

[40] D. Kudo and H. Tajima, arXiv:2205.03245 [quant-ph] (2022).
https://doi.org/10.48550/arXiv.2205.03245
arXiv:2205.03245

[41] J. A. Vaccaro, F. Anselmi, H. M. Wiseman, and K. Jacobs, Physical Review A 77, 032114 (2008).
https://doi.org/10.1103/PhysRevA.77.032114

[42] G. Gour, I. Marvian, and R. W. Spekkens, Physical Review A 80, 012307 (2009).
https://doi.org/10.1103/PhysRevA.80.012307

[43] I. Marvian Mashhad, Symmetry, Asymmetry and Quantum Information, Ph.D. thesis, University of Waterloo (2012).
https://uwspace.uwaterloo.ca/handle/10012/7088

[44] G. Gour, D. Jennings, F. Buscemi, R. Duan, and I. Marvian, Nature Communications 9, 5352 (2018).
https://doi.org/10.1038/s41467-018-06261-7

[45] K. Yamaguchi and H. Tajima, “Beyond i.i.d. in the Resource Theory of Asymmetry: An Information-Spectrum Approach for Quantum Fisher Information,” (2022), arXiv:2204.08439 [cond-mat, physics:quant-ph].
https://doi.org/10.48550/arXiv.2204.08439
arXiv:2204.08439

[46] G. Gour, PRX Quantum 3, 040323 (2022).
https://doi.org/10.1103/PRXQuantum.3.040323

[47] I. Marvian, Physical Review Letters 129, 190502 (2022).
https://doi.org/10.1103/PhysRevLett.129.190502

[48] R. Renner and S. Wolf, in International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings. (2004) pp. 233–.
https://doi.org/10.1109/ISIT.2004.1365269

[49] R. Renner, Security of Quantum Key Distribution, PhD Thesis, ETH Zurich (2005).
https://doi.org/10.48550/arXiv.quant-ph/0512258
arXiv:quant-ph/0512258

[50] E. H. Lieb and J. Yngvason, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, 20130408 (2013).
https://doi.org/10.1098/rspa.2013.0408

[51] M. Keyl and R. F. Werner, Journal of Mathematical Physics 40, 3283 (1999).
https://doi.org/10.1063/1.532887

[52] E. A. Morozova and N. N. Chentsov, Itogi Nauki i Tekhniki 36, 69 (1989).

[53] D. Petz, Linear Algebra and its Applications 244, 81 (1996).
https://doi.org/10.1016/0024-3795(94)00211-8

[54] F. Kubo and T. Ando, Mathematische Annalen 246, 205 (1980).
https://doi.org/10.1007/BF01371042

[55] D. Petz, Quantum Information Theory and Quantum Statistics, Theoretical and Mathematical Physics (Springer, Berlin, Heidelberg, 2008).
https://doi.org/10.1007/978-3-540-74636-2

[56] P. Gibilisco and T. Isola, Journal of Mathematical Analysis and Applications 375, 270 (2011).
https://doi.org/10.1016/j.jmaa.2010.09.029

[57] D. Petz and C. Ghinea, in Quantum Probability and Related Topics, QP-PQ: Quantum Probability and White Noise Analysis, Vol. Volume 27 (WORLD SCIENTIFIC, 2011) pp. 261–281.
https://doi.org/10.1142/9789814338745_0015

[58] G. Tóth and D. Petz, Physical Review A 87, 032324 (2013).
https://doi.org/10.1103/PhysRevA.87.032324

[59] S. Yu, arXiv:1302.5311 [quant-ph] (2013).
https://doi.org/10.48550/arXiv.1302.5311
arXiv:1302.5311

[60] P. Gibilisco, D. Imparato, and T. Isola, Proceedings of the American Mathematical Society 137, 317 (2009).
https://doi.org/10.1090/S0002-9939-08-09447-1

[61] E. H. Lieb, Advances in Mathematics 11, 267 (1973).
https://doi.org/10.1016/0001-8708(73)90011-X

[62] M. Horodecki, P. Horodecki, and R. Horodecki, Physical Review Letters 84, 2014 (2000).
https://doi.org/10.1103/PhysRevLett.84.2014

[63] M. J. Donald, M. Horodecki, and O. Rudolph, Journal of Mathematical Physics 43, 4252 (2002).
https://doi.org/10.1063/1.1495917

[64] M. Plenio and S. Virmani, Quantum Information and Computation 7, 1 (2007).
https://doi.org/10.26421/QIC7.1-2-1

[65] T. S. Han, Information-Spectrum Methods in Information Theory, Stochastic Modelling and Applied Probability, Vol. 50 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2003).
https://doi.org/10.1007/978-3-662-12066-8

[66] N. Datta and R. Renner, IEEE Transactions on Information Theory 55, 2807 (2009).
https://doi.org/10.1109/TIT.2009.2018340

[67] N. Datta, IEEE Transactions on Information Theory 55, 2816 (2009).
https://doi.org/10.1109/TIT.2009.2018325

[68] M. Hayashi, in IEEE International Symposium on Information Theory, 2003. Proceedings. (2003) pp. 431–.
https://doi.org/10.1109/ISIT.2003.1228448

[69] G. Bowen and N. Datta, IEEE Transactions on Information Theory 54, 3677 (2008).
https://doi.org/10.1109/TIT.2008.926377

[70] G. Vidal, Journal of Modern Optics 47, 355 (2000).
https://doi.org/10.1080/09500340008244048

[71] M. Horodecki, Quantum Information and Computation 1, 3 (2001).
https://doi.org/10.26421/QIC1.1-2

[72] B. Synak-Radtke and M. Horodecki, Journal of Physics A: Mathematical and General 39, L423 (2006).
https://doi.org/10.1088/0305-4470/39/26/L02

[73] M. Fannes, Communications in Mathematical Physics 31, 291 (1973).
https://doi.org/10.1007/BF01646490

[74] D. Janzing, P. Wocjan, R. Zeier, R. Geiss, and T. Beth, International Journal of Theoretical Physics 39, 2717 (2000).
https://doi.org/10.1023/A:1026422630734

[75] M. Horodecki and J. Oppenheim, Nature Communications 4, 2059 (2013).
https://doi.org/10.1038/ncomms3059

[76] M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information: 10th Anniversary Edition,” (2010).
https://doi.org/10.1017/CBO9780511976667

[77] A. D. Barbour and V. Ćekanavićius, The Annals of Probability 30, 509 (2002).
https://doi.org/10.1214/aop/1023481001

Cited by

[1] Koji Yamaguchi and Hiroyasu Tajima, “Beyond i.i.d. in the Resource Theory of Asymmetry: An Information-Spectrum Approach for Quantum Fisher Information”, arXiv:2204.08439, (2022).

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Source: https://quantum-journal.org/papers/q-2023-05-22-1012/

Time Stamp: May 22, 2023

Time Stamp: Aug 23, 2022

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