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The quantification and characterization of non-Markovian dynamics in quantum systems is an essential endeavor both for the theory of open quantum systems and for a deeper understanding of the effects of non-Markovian noise on quantum technologies.
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F. F. Fanchini, G. Karpat, B. Çakmak, L. K. Castelano, G. H. Aguilar, O. J. Farías, S. P. Walborn, P. H. S. Ribeiro, and M. C. de Oliveira, Phys. Rev. Lett. 112
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In Refs. Bhattacharya et al. 2018 ; Bhattacharya and Bhattacharya 2018 , the authors construct a resource theory for non-Markovianity where they identify the set of free states as the Choi-Jamałkowski matrices corresponding to Markovian maps. Although this construction is in some ways easier to work with, since there are both designated free states and free operations, this quickly leads into difficulties. Any resourceful operation can transform a free state (a Choi matrix for a Markovian map, which is normalized and positive semidefinite) into a non-state (since it can now have negative eigenvalues) and so it can take us outside the set of quantum states, which is usually assumed to be the landscape for quantum resource theories. To circumvent such obstacles, we avoid such an identification and only define a set of free operations
2018
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J. Watrous, The Theory of Quantum Information , 1st ed. (Cambridge University Press, 2018)
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B. Regula, Journal of Physics A: Mathematical and Theoretical 51
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E. Chitambar and G. Gour, Rev. Mod. Phys. 91
2019
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R. Takagi, B. Regula, K. Bu, Z.-W. Liu, and G. Adesso, Phys. Rev. Lett. 122
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P. Skrzypczyk and N. Linden, Phys. Rev. Lett. 122
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