Abstract
At first, a short account is given of some basic notations and results on parallel transport along mixed states. A new connection form (gauge field) is introduced to give a geometric meaning to the concept of parallelity in the theory of density operators.
Similar content being viewed by others
References
Uhlmann, A., Rep. Math. Phys. 24, 229 (1986).
Berry, M. V., Proc. R. Soc. Lond. A392, 45 (1984).
Simon, B., Phys. Rev. Lett. 51, 2167 (1983).
Wilczek, F. and Zee, A., Phys. Rev. Lett. 52, 2111 (1984).
Bures, D. J. C., Trans Amer. Math. Soc. 135, 119 (1969).
Uhlmann, A., Rep. Math. Phys. 9, 273 (1976); Araki, H. and Raggio, G. A., Lett. Math. Phys. 6, 237 (1982); Alberti, P. M. and Uhlmann, A., Lett. Math. Phys. 7, 107 (1983).
Dabrowski, L., A superposition principle for mixed states?, SISSA, Trieste, 156/88/FM.
Uhlmann, A., Parallel transport and holonomy along density operators, in H. D.Doebner and J. D.Henning (eds), Differential Geometric Methods in Theoretical Physics, World Scientific, Singapore, 1987, pp. 246–254.
Dabrowski, L. and Jadczyk, A., Quantum statistical holonomy, Trieste PL-50125 (1988).
Dabrowski, L. and Grosse, H., On quantum holonomy for mixed states, Vienna UWThPh-1988-36.
Uhlmann, A., Ann. Phys. 47, 63 (1989).