arXiv 0911.26332009-11-13quant-ph

量子脉冲位置调制理论及相关数值问题

Theory of Quantum Pulse Position Modulation and Related Numerical Problems

G. Cariolaro, G. Pierobon

备注：: 10 pages, 7 figures, accepted for publication in IEEE Trans. on Communications

摘要：

本文利用相干激光辐射的Glauber表示讨论了在无热噪声（纯态）和有热噪声（混合态）情况下的量子脉冲位置调制（PPM）。我们的目标是找到最佳（或次优）的测量算子，并评估相应的错误概率。对于PPM，量子态的正确表述是由m个恒等希尔伯特空间的张量积给出的，其中m是PPM阶。混合状态的存在，由于热噪声，产生一个优化问题，涉及矩阵的巨大的维度，这已经为4-PPM，是一万的顺序。为了克服这种计算的复杂性，目前可用的量子检测方法，这是基于显式的结果，凸线性规划和平方根测量，比较，找到计算成本较低的一个。在本文中，量子PPM格式的几何均匀对称性发挥了重要作用。错误概率的评估证实了量子检测相对于经典检测的巨大优越性。

英文摘要：

The paper deals with quantum pulse position modulation (PPM), both in the absence (pure states) and in the presence (mixed states) of thermal noise, using the Glauber representation of coherent laser radiation. The objective is to find optimal (or suboptimal) measurement operators and to evaluate the corresponding error probability. For PPM, the correct formulation of quantum states is given by the tensorial product of m identical Hilbert spaces, where m is the PPM order. The presence of mixed states, due to thermal noise, generates an optimization problem involving matrices of huge dimensions, which already for 4-PPM, are of the order of ten thousand. To overcome this computational complexity, the currently available methods of quantum detection, which are based on explicit results, convex linear programming and square root measurement, are compared to find the computationally less expensive one. In this paper a fundamental role is played by the geometrically uniform symmetry of the quantum PPM format. The evaluation of error probability confirms the vast superiority of the quantum detection over its classical counterpart.

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