State and dynamical parameter estimation for open quantum systems
Author(s)
Gambetta, J
Wiseman, HM
Griffith University Author(s)
Year published
2001
Metadata
Show full item recordAbstract
Following evolution of an open quantum system one requires full knowledge of its dynamics. In this paper we consider open quantum systems for which the Hamiltonian is "uncertain." In particular, we treat in detail a simple system similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]: a radiatively damped atom driven by an unknown Rabi frequency O (as would occur for an atom at an unknown point in a standing light wave). By measuring the environment of the system, knowledge about the system state, and about the uncertain dynamical parameter, can be acquired. We find that these two sorts of knowledge ...
View more >Following evolution of an open quantum system one requires full knowledge of its dynamics. In this paper we consider open quantum systems for which the Hamiltonian is "uncertain." In particular, we treat in detail a simple system similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]: a radiatively damped atom driven by an unknown Rabi frequency O (as would occur for an atom at an unknown point in a standing light wave). By measuring the environment of the system, knowledge about the system state, and about the uncertain dynamical parameter, can be acquired. We find that these two sorts of knowledge acquisition (quantified by the posterior distribution for O, and the conditional purity of the system, respectively) are quite distinct processes, which are not strongly correlated. Also, the quality and quantity of knowledge gain depend strongly on the type of monitoring scheme. We compare five different detection schemes (direct, adaptive, homodyne of the x quadrature, homodyne of the y quadrature, and heterodyne) using four different measures of the knowledge gain (Shannon information about O, variance in O, long-time system purity, and short-time system purity).
View less >
View more >Following evolution of an open quantum system one requires full knowledge of its dynamics. In this paper we consider open quantum systems for which the Hamiltonian is "uncertain." In particular, we treat in detail a simple system similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]: a radiatively damped atom driven by an unknown Rabi frequency O (as would occur for an atom at an unknown point in a standing light wave). By measuring the environment of the system, knowledge about the system state, and about the uncertain dynamical parameter, can be acquired. We find that these two sorts of knowledge acquisition (quantified by the posterior distribution for O, and the conditional purity of the system, respectively) are quite distinct processes, which are not strongly correlated. Also, the quality and quantity of knowledge gain depend strongly on the type of monitoring scheme. We compare five different detection schemes (direct, adaptive, homodyne of the x quadrature, homodyne of the y quadrature, and heterodyne) using four different measures of the knowledge gain (Shannon information about O, variance in O, long-time system purity, and short-time system purity).
View less >
Journal Title
Physical Review A: Atomic, Molecular and Optical Physics
Volume
64
Issue
4
Publisher URI
Copyright Statement
© 2001 American Physical Society. Reproduced in accordance with the copyright policy of the publisher. This journal is available online - use hypertext links.
Subject
Mathematical sciences
Physical sciences
Chemical sciences