被动线性量子系统的维纳滤波
Wiener Filtering for Passive Linear Quantum Systems
AI总结：
本文研究被动线性量子系统的维纳滤波均衡问题，发现均方最优量子均衡滤波器对应非凸约束优化问题，且与经典均衡不同，存在噪声方差阈值，低于该阈值无法保证均方误差改善。
摘要：
本文考虑用于被动线性量子系统均衡的维纳滤波问题的一个版本。我们证明，考虑所涉及信号的量子特性会导致经典均衡问题中通常不会遇到的特征。最显著的是，寻找均方最优量子均衡滤波器相当于求解一个非凸约束优化问题。我们讨论了两种解决该问题的方法，两者都涉及对约束的松弛。在这两种情况下，与经典均衡不同，存在一个噪声方差的阈值，低于该阈值时无法保证均方误差的改善。
英文摘要：
This paper considers a version of the Wiener filtering problem for equalization of passive quantum linear quantum systems. We demonstrate that taking into consideration the quantum nature of the signals involved leads to features typically not encountered in classical equalization problems. Most significantly, finding a mean-square optimal quantum equalizing filter amounts to solving a nonconvex constrained optimization problem. We discuss two approaches to solving this problem, both involving a relaxation of the constraint. In both cases, unlike classical equalization, there is a threshold on the variance of the noise below which an improvement of the mean-square error cannot be guaranteed.
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