高斯量子过程的性质及其应用
Properties and Application of Gaussian Quantum Processes
摘要：
高斯态、操作和测量是连续变量量子信息处理的核心构建块，这为丰富的应用铺平了道路，特别是包括基于网络的量子计算和通信。为了充分利用高斯过程，需要理解和利用合适的数学工具，如辛空间，辛代数和维格纳表示。将这些数学工具应用到实际的量子场景中，我们开发了各种量子转换方案，基于干涉的玻色子模式置换和玻色子传感。我们证明了高斯幺正过程的一般耦合器可以转换成高保真度的换能器，假设访问无限压缩和自适应前馈与零差测量。为了解决有限压缩的实际限制，我们探索了基于干涉的协议。这些协议让我们自由地置换玻色子模式，只有假设访问单模高斯运算和多个使用一个给定的多模高斯过程。因此，这样的方案不仅能够实现玻色子系统的通用解耦，这对于抑制系统与环境之间的不期望的耦合是有用的，而且还能够实现忠实的双向单模量子转导。此外，注意到高斯过程是光学传感器的合适的理论模型，我们研究了光学参数传感的量子噪声理论及其在提供大的测量精度提高的潜力。我们还将高斯理论扩展到离散变量系统，并给出了量子（门）隐形传态等几个例子。这些分析都是从量子对易关系出发的，因而具有广泛的适用性。
英文摘要：
Gaussian states, operations, and measurements are central building blocks for continuous-variable quantum information processing which paves the way for abundant applications, especially including network-based quantum computation and communication. To make the most use of the Gaussian processes, it is required to understand and utilize suitable mathematical tools such as the symplectic space, symplectic algebra, and Wigner representation. Applying these mathematical tools to practical quantum scenarios, we developed various schemes for quantum transduction, interference-based bosonic mode permutation and bosonic sensing. We demonstrated that generic coupler characterized by Gaussian unitary process can be transformed into a high-fidelity transducer, assuming the access to infinite squeezing and adaptive feedforward with homodyne measurements. To address the practical limitation of finite squeezing, we explored the interference-based protocols. These protocols let us freely permute bosonic modes only assuming the access to single-mode Gaussian operations and multiple uses of a given multi-mode Gaussian process. Thus, such a scheme not only enables universal decoupling for bosonic systems, which is useful for suppressing undesired coupling between the system and the environment, but also faithful bidirectional single-mode quantum transduction. Moreover, noticing that the Gaussian processes are appropriate theoretical models for optical sensors, we studied the quantum noise theory for optical parameter sensing and its potential in providing great measurement precision enhancement. We also extended the Gaussian theories to discrete variable systems, with several examples such as quantum (gate) teleportation. All the analyses originated from the fundamental quantum commutation relations, and therefore are widely applicable.
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