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We provide a general framework for the identification of open quantum systems.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information
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P. Lemke, S. S. Skiena, and W. D. Smith, “Reconstructing Sets from Interpoint Distances,” DIMACS Technical Reports 2002-37 (2002)
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Quantum State Estimation
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R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications
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G. Dirr and U. Helmke, GAMM-Mitt. 31
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E. D. Sontag, Y. Wang, and A. Megretski, IEEE Trans. Autom. Control 54
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This is not really a constraint: if some superoperator is corresponding to a unitary dynamics, − i [ H , ⋅ ] -i[H,{}\cdot{}\,] , simply include a further term i [ H , ⋅ ] i[H,{}\cdot{}\,] and an extra control to the summation in ( 1
Cited in the paper.
This can be generalized to POVMs easily, but yields no further insight
Cited in the paper.
M. M. Wolf, “Quantum Channels & Operations: Guided Tour,” URL: https://www-m5.ma.tum.de/foswiki/pub/ M5/Allgemeines/MichaelWolf/QChannelLecture.pdf
Cited in the paper.
Note that not every vector r → \vec{r} corresponds to a valid density matrix ρ \rho , since ρ \rho needs to be positive semi-definite. In particular, all r → \vec{r} of valid ρ \rho satisfy | r → | ≤ 1 |\vec{r}|\leq 1 , with pure states represented by vectors of unit length | r → | = 1 |\vec{r}|=1 , while the converse is not necessarily true: there exist vectors that satisfy | r → | ≤ 1 |\vec{r}|\leq 1 but do not correspond to any physical ρ \rho . See G. Kimura, Phys. Lett. A 314
Cited in the paper.
This follows from the invertibility of the time-dependent Markovian maps
Cited in the paper.
Nonetheless it is an intriguing problem to characterize the reachable operations. See C. O’Meara, G. Dirr, and T. Schulte-Herbruggen, IEEE Trans. Autom. Control 57
2012
Later among the works it cites.
M. Guţă and N. Yamamoto, arXiv:1303.3771 [quant-ph] (2013)
2013
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2013
Later among the works it cites.
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