Abstract We define the resource non-increasing (RNI) framework to study the dynamical resource theory. With this definition, we propose several potential quantification candidates under various free operation sets. For explicit demonstrations, we quantify the quantum dynamical coherence in the scenarios with and without post-selective measurements. Correspondingly, we show that the maximally incoherent operations (MIO) and the incoherent operations (IO) in the static coherence resource theory are free in the sense of dynamical coherence. We also provide operational meanings for the measures by the quantum discrimination tasks. Moreover, for the dynamical total coherence, we also present convenient measures and give the analytic calculation for the amplitude damping channel.
Si-Ren Yang(杨思忍) and Chang-Shui Yu(于长水) Quantum dynamical resource theory under resource non-increasing framework 2023 Chin. Phys. B 32 040305
[1] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys.81 865 [2] Vedral V, Plenio M B, Rippin M A and Knight P L 1997 Phys. Rev. Lett.78 2275 [3] Girolami D and Yadin B 2017 Entropy19 124 [4] Yu C S and Song H S 2009 Phys. Rev. A80 022324 [5] Ollivier H and Zurek W H 2001 Phys. Rev. Lett.88 017901 [6] Datta A, Shaji A and Caves C M 2008 Phys. Rev. Lett.100 050502 [7] Cavalcanti D, Aolita L, Boixo S, Modi K, Piani M and Winter A 2010 Phys. Rev. A83 483 [8] Luo S 2008 Phys. Rev. A77 042303 [9] Giorda P and Paris M G A 2010 Phys. Rev. Lett.105 020503 [10] Baumgratz T, Cramer M and Plenio M B 2014 Phys. Rev. Lett.113 140401 [11] Brunner N, Cavalcanti D, Pironio S, Scarani V and Wehner S 2014 Rev. Mod. Phys.86 419 [12] Kirchmair G, Zähringer F, Gerritsma R, Kleinmann M, Gühne O, Cabello A, Blatt R and Roos C F 2009 Nature460 494 [13] Strobel H, Muessel W, Linnemann D, Zibold T, Hume D B, Pezzé L, Smerzi A and Oberthaler M K 2014 Science345 424 [14] Marvian I and Spekkens R 2014 Nat. Commun.5 3821 [15] Yu X D, Zhang D J, Xu G F and Tong D M 2016 Phys. Rev. A94 060302 [16] Rana S, Parashar P and Lewenstein M 2016 Phys. Rev. A93 012110 [17] Yao Y, Xiao X, Ge L and Sun C P 2015 Phys. Rev. A92 022112 [18] Zhao H Q and Yu C S 2018 Sci. Rep.8 299 [19] Yu C S 2017 Phys. Rev. A95 042337 [20] Bu K, Singh U, Fei S M, Pati A K and Wu J 2017 Phys. Rev. Lett.119 150405 [21] Wu Z, Zhang L, Fei S M and Li-Jost X 2020 J. Phys. A: Math. Theor.54 015302 [22] Winter A and Yang D 2016 Phys. Rev. Lett.116 120404 [23] Napoli C, Bromley T R, Cianciaruso M, Piani M, Johnston N and Adesso G 2016 Phys. Rev. Lett.116 150502 [24] Rana S, Parashar P, Winter A and Lewenstein M 2017 Phys. Rev. A96 052336 [25] Zhu H, Hayashi M and Chen L 2018 Phys. Rev. A97 022342 [26] Patel D, Patro S, Vanarasa C, Chakrabarty I and Pati A K 2021 Phys. Rev. A103 022422 [27] Marvian I, Spekkens R W and Zanardi P 2016 Phys. Rev. A93 052331 [28] Piani M, Cianciaruso M, Bromley T R, Napoli C, Johnston N and Adesso G 2016 Phys. Rev. A93 042107 [29] Ioffe L and Mézard M 2007 Phys. Rev. A75 032345 [30] Korzekwa K, Czachórski S, Puchala Z and Życzkowski K 2018 New J. Phys.20 043028 [31] Wang X, Wilde M M and Su Y 2019 New J. Phys.21 103002 [32] Bischof F, Kampermann H and Bruß D 2019 Phys. Rev. Lett.123 110402 [33] Saxena G, Chitambar E and Gour G 2020 Phys. Rev. Res.2 023298 [34] Xu J 2021 Phys. Lett. A387 127028 [35] Gour G and Scandolo C M 2020 Phys. Rev. Lett.125 180505 [36] Theurer T, Satyajit S and Plenio M B 2020 Phys. Rev. Lett.125 130401 [37] Chitambar E and Gour G 2019 Rev. Mod. Phys.91 025001 [38] Liu Y and Yuan X 2020 Phys. Rev. Res.2 012035 [39] Kuroiwa K and Yamasaki H 2020 Quantum4 355 [40] Díaz M G, Desef B, Rosati M, Egloff D, Calsamiglia J, Smirne A, Skotiniotis M and Huelga S F 2020 Quantum4 249 [41] Designolle S, Uola R, Luoma K and Brunner N 2021 Phys. Rev. Lett.126 220404 [42] Gour G and Winter A 2019 Phys. Rev. Lett.123 150401 [43] Masini M, Theurer T and Plenio M B 2021 Phys. Rev. A103 042426 [44] Hsieh C Y 2021 PRX Quantum2 020318 [45] Theurer T, Egloff D, Zhang L and Plenio M B 2019 Phys. Rev. Lett.122 190405 [46] Mani A and Karimipour V 2015 Phys. Rev. A92 032331 [47] Yang S R and Yu C S 2018 Ann. Phys.388 305 [48] Yu C S, Yang S R and Guo B Q 2016 Quantum Inf. Proc.15 3773 [49] Nielsen M A and Chuang I 2000 Quantum computation and quantum information (Cambridge: Cambridge University Press) [50] Yang S R and Yu C S 2021 arXiv: 2110.14267 [51] Chiribella G, D'Ariano G M and Perinotti P 2008 Phys. Rev. Lett.101 180501 [52] Cooney T, Mosonyi M and Wilde M M 2016 Commun. Math. Phys.344 797 [53] Hayashi M 2009 IEEE Trans. Inf. Theor.55 3807 [54] Duan R, Feng Y and Ying M 2009 Phys. Rev. Lett.103 210501 [55] Matthews W, Wehner S and Winter A 2009 Commun. Math. Phys.291 813 [56] Choi M D 1975 Linear Algebra Appl.10 285 [57] Jamio lkowski A 1972 Rep. Math. Phys.3 275 [58] Khachiyan L 1980 USSR Comput. Math. Phys.20 53 [59] Watrous J 2018 The Theory of Quantum Information (Cambridge: Cambridge university press) [60] Giorgi G and Kjeldsen T H 2014 Traces and Emergence of Nonlinear Programming (New York: Springer) [61] Grant M and Boyd S Cvx: Matlab software for disciplined convex programming
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
