We present optimal schemes, based on photon number measurements, for Gaussian state tomography and for Gaussian process tomography. An $n$-mode Gaussian state is completely specified by $2n^2+3n$ parameters. Our scheme requires exactly $2n^2+3n$ distinct photon number measurements to tomograph the state and is therefore optimal. Further, we describe an optimal scheme to characterize Gaussian processes by using coherent state probes and photon number measurements. With much recent progress in photon number measurement experimental techniques, we hope that our scheme will be useful in various quantum information processing protocols including entanglement detection, quantum computation, quantum key distribution and quantum teleportation. This work builds upon the work of Parthasarathy .

中文翻译：

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使用光子数分辨探测器对高斯通道进行最佳表征

我们提出基于光子数测量，高斯状态层析成像和高斯过程层析成像的最佳方案。一个$ñ$-模式高斯状态完全由 $2{ñ}^2+3ñ$参数。我们的计划要求$2{ñ}^2+3ñ$不同的光子数量测量以对状态进行断层成像，因此是最佳的。此外，我们描述了一种通过使用相干态探测器和光子数测量来表征高斯过程的最佳方案。随着光子数测量实验技术的最新进展，我们希望我们的方案可用于各种量子信息处理协议中，包括纠缠检测，量子计算，量子密钥分配和量子隐形传态。这项工作建立在帕萨萨拉西的工作之上。