Abstract
We give an explicit parameterization for the state space of an n-level density matrix. The parameterization is based on the canonical coset decomposition of unitary matrices. As an application, we also calculate explicitly the Bures metric tensor over the state space of two-level quantum system.
Similar content being viewed by others
References
L. J. Boya, M. Byrd, M. Mims, and E. C. G. Sudarshan, quant-ph/9810084.
M. S. Byrd, J. Math. Phys. 39, 6125 (1998); ibid. 41, 1026 (2000) Erratum.
M. S. Byrd and P. Slater, Phys. Lett. A 283, 152 (2001).
T. Tilma, M. Byrd, and E. C. G. Sudarshan, J. Phys. A: Math. Gen. 35, 10445 (2002).
T. Tilma and E. C. G. Sudarshan, J. Phys. A: Math. Gen. 35, 10467 (2002).
T. Tilma and E. C. G. Sudarshan, J. Geom. Phys. 52, 263 (2004).
K. Życzkowski and W. Słomczyński, J. Phys. A: Math. Gen. 34, 6689 (2001).
S. J. Akhtarshenas and M. A. Jafarizadeh, Quantum Inf. Comput. 3, 229 (2003).
W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
R. Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications (John-Wiley Publishing Co., 1974).
D. J. C. Bures, Trans. Am. Math. Phys. 135, 199 (1969).
A. Uhlmann, Rep. Math. Phys. 9, 273 (1976).
R. Jozsa, J. Mod. Opt. 41, 2315 (1994).
M. Hübner, Phys. Lett. A 163, 239 (1992).
J. Dittmann, Sem. Sophus Lie 3, 73 (1993).
J. Dittmann, J. Phys. A: Math. Gen. 32, 2663 (1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
The text was submitted by the author in English.