dorsal/arxiv
View SchemaState and dynamical parameter estimation for open quantum systems
| Authors | Jay Gambetta, H. M. Wiseman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103032 |
| URL | https://arxiv.org/abs/quant-ph/0103032 |
| DOI | 10.1103/PhysRevA.64.042105 |
| Journal | Phys. Rev. A 64, 042105 (2001) |
Abstract
Following the evolution of an open quantum system 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 $\Omega$ (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 $\Omega$, 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 $\Omega$, variance in $\Omega$, long-time system purity, and short-time system purity).
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"abstract": "Following the evolution of an open quantum system requires full knowledge of\nits dynamics. In this paper we consider open quantum systems for which the\nHamiltonian is ``uncertain\u0027\u0027. In particular, we treat in detail a simple system\nsimilar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]:\na radiatively damped atom driven by an unknown Rabi frequency $\\Omega$ (as\nwould occur for an atom at an unknown point in a standing light wave). By\nmeasuring the environment of the system, knowledge about the system state, and\nabout the uncertain dynamical parameter, can be acquired. We find that these\ntwo sorts of knowledge acquisition (quantified by the posterior distribution\nfor $\\Omega$, and the conditional purity of the system, respectively) are quite\ndistinct processes, which are not strongly correlated. Also, the quality and\nquantity of knowledge gain depend strongly on the type of monitoring scheme. We\ncompare five different detection schemes (direct, adaptive, homodyne of the $x$\nquadrature, homodyne of the $y$ quadrature, and heterodyne) using four\ndifferent measures of the knowledge gain (Shannon information about $\\Omega$,\nvariance in $\\Omega$, long-time system purity, and short-time system purity).",
"arxiv_id": "quant-ph/0103032",
"authors": [
"Jay Gambetta",
"H. M. Wiseman"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.64.042105",
"journal_ref": "Phys. Rev. A 64, 042105 (2001)",
"title": "State and dynamical parameter estimation for open quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0103032"
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