arXiv quant-ph/05032222005-03-29quant-ph

QED腔中高非线性模型的量子投影滤波器

Quantum projection filter for a highly nonlinear model in cavity QED

Ramon van Handel, Hideo Mabuchi

备注：: 19 pages, 6 figures. A version with high quality images can be found at http://minty.caltech.edu/papers.php
发表信息：: J. Opt. B: Quantum Semiclass. Opt. 7 (2005) S226-S236.
DOI：: 10.1088/1464-4266/7/10/005

摘要：

在经典和量子随机控制理论中，滤波方程都发挥着重要作用，它递归地更新所观察系统的信息状态。不幸的是，该理论受到信息状态的无限维性的困扰，这严重限制了它的实际适用性，除了在少数情况下（例如线性高斯情况）。经典滤波理论中提出的一种解决方案是投影滤波器。在该方案中，过滤器被限制为通过相对于Fisher度量的切空间上的正交投影在有限维密度族中演化。在这里，我们将这种方法应用到一个简单的，但高度非线性的量子模型的光学相位双稳态的强耦合的二能级原子在光学腔。我们观察到量子投影滤波器的近最佳性能，证明了这种方法的实用性。

英文摘要：

Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by infinite-dimensionality of the information state which severely limits its practical applicability, except in a few select cases (e.g. the linear Gaussian case.) One solution proposed in classical filtering theory is that of the projection filter. In this scheme, the filter is constrained to evolve in a finite-dimensional family of densities through orthogonal projection on the tangent space with respect to the Fisher metric. Here we apply this approach to the simple but highly nonlinear quantum model of optical phase bistability of a stongly coupled two-level atom in an optical cavity. We observe near-optimal performance of the quantum projection filter, demonstrating the utility of such an approach.

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