Abstract
This paper collects miscellaneous results about the group SU(1, 1) that are helpful in applications in quantum optics. Moreover, we derive two new results, the first of which is about the approximability of SU(1, 1) elements by a finite set of elementary gates and the second of which is about the regularization of group identities for tomographic purposes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. W. Boyd, Nonlinear Optics (Elsevier, Sand Diego, 2003).
H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
D. F. Walls, Nature 306, 141 (1983).
C. M. Caves and P. D. Drummond, Rev. Mod. Phys. 66, 481 (1994).
S. L. Braunstein and H. J. Kimble, Phys. Rev. Lett. 80, 869872 (1998).
G. M. D’Ariano, E. De Vito, and L. Maccone, Phys. Rev. A 64, 033805 (2001).
M. Duflo and C. C. Moore, J. Funct. Anal. 21, 209 (1976).
A. L. Carey, Bull. Aust. Math. Soc. 15, 1 (1976).
R. R. Puri, Mathematical Methods of Quantum Optics (Springer, Heidelberg, 2001).
A. Grossmann, J. Morlet, and T. Pauli, J. Math. Phys. 26, 2473 (1985).
A. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Heidelberg, 1986).
Author information
Authors and Affiliations
Additional information
Original Text © Astro, Ltd., 2006.
Rights and permissions
About this article
Cite this article
Chiribella, G., D’Ariano, G.M. & Perinotti, P. Applications of the group SU(1, 1) for quantum computation and tomography. Laser Phys. 16, 1572–1581 (2006). https://doi.org/10.1134/S1054660X06110119
Received:
Issue Date:
DOI: https://doi.org/10.1134/S1054660X06110119