Abstract
In this work, we study an inverse dynamical problem for a bipartite quantum system governed by the time local master equation: to find the class of generators which give rise to a certain time evolution with the constraint of fixed reduced states (marginals). The compatibility of such choice with a global unitary evolution is considered. For the nonunitary case, we propose a systematic method to reconstruct examples of master equations and address them to different physical scenarios.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. S. Glaser, Eur. Phys. J. D, 69, 22 (2015).
S. G. Schirmer, H. Fu, and A. I. Solomon, Phys. Rev. A, 63, 063410 (2001).
H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control, Cambridge University Press (2009).
C. Altafini and F. Ticozzi, IEEE Trans. Autom. Control, 57, 1898 (2012).
M. Walter, B. Doran, D. Gross, and M. Christandl, Science, 340, 1205 (2013).
C. Schilling, C. L. Benavides-Riveros, and P. Vrana, Phys. Rev. A, 96, 052312 (2017).
R. Chakraborty and D. A. Mazziotti, Phys. Rev. A, 91, 010101 (2015).
S. G. Schirmer, “Hamiltonian engineering for quantum systems,” in: Proceedings of the 3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control (Nagoya, Japan, 2006).
H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press (2006).
J. Bernatska and A. Messina, Phys. Scr., 85, 015001 (2012).
J. Bernatska and P. Holod, in: Proceedings of the 9th International Conference “Geometry, Integrability and Quantization (Sofia, 2008), p. 146.
D. Chruściński, Open Syst. Inform. Dyn., 21, 1440004 (2014).
A. Rivas and S. F. Huelga, Open Quantum Systems: An Introduction, Springer, Berlin (2011).
A. A. Klyachko, J. Phys. Conf. Ser., 36, 72 (2006).
C. Schilling, Quantum Marginal Problem and Its Physical Relevance, PhD Thesis at ETH Zurich (2014).
A. Sawicki, M. Walter, and M. Kuś, J. Phys. A: Math. Gen., 46, 5 (2013).
E. Brüning, H. Mäkelä, A. Messina, and F. Petruccione, J. Mod. Opt., 59, 1 (2012).
I. G. Macdonald, Symmetric Functions and Hall Polynomials, Second Edition, Oxford University Press (1995).
R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications, Springer, Berlin (1987).
V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys., 17, 821 (1976).
G. Lindblad, Comm. Math. Phys., 48, 119 (1976).
U. Fano, Rev. Mod. Phys., 55, 855 (1983).
G. Kimura, Phys. Lett. A, 314, 339 (2003).
S. Luo, Phys. Rev. A, 77, 042303 (2008).
R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed., Cambridge University Press (2013).
B. Hall, Lie Groups, Lie Algebras, and Representations, An Elementary Introduction, Second Edition , Springer, Heidelberg (2015).
S. C. Hou, X. X Yi, S. X. Yu, and C. H. Oh, Phys. Rev. A, 83, 062115 (2011).
H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett., 103, 210401 (2009).
D. Chruściński, A. Kossakowski, and A. Rivas, Phys. Rev. A, 83, 052128 (2011).
V. Buzek, Phys. Rev. A, 58, 1723 (1998).
R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys., 81, 865 (2009).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Baio, G., Chruściński, D. & Messina, A. A Possible Time-Dependent Generalization of the Bipartite Quantum Marginal Problem. J Russ Laser Res 39, 422–437 (2018). https://doi.org/10.1007/s10946-018-9737-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-018-9737-x