AI 中文总结
该研究提出确定性光子损耗子空间（DPLS）理论，揭示有损耗光学系统中量子相干性、退相干与光子数减少的相互作用，可用于精确控制量子干涉及相关量子信息处理。
AI 中文摘要
量子相干性、量子退相干与光子数减少在有损耗的线性光学系统中并存，但三者如何共同决定量子光的演化仍不清楚。本文基于奇异值分解（SVD），提出了有损耗系统中量子干涉的确定性光子损耗子空间（DPLS）理论。通过对奇异值为0或1的散射矩阵进行SVD，首先定义了一系列完全损耗和无损耗的输入模式。根据第1至第i个损耗模式中的n₁,…,nᵢ个光子，输入态的希尔伯特空间可分解为一组正交子空间H_((n₁,…,n_i ))^in，即确定性光子损耗子空间（DPLSs）。建立DPLS概念后，输入态可投影到这些DPLSs上。在每个DPLS中，损耗模式中的光子会完全耗散，而无损耗模式中的光子则经历幺正演化。由于退相干是并发过程，输出态是所有投影演化结果的统计混合。接着，基于DPLS理论，本文不仅重新研究了反HOM（Anti-HOM）干涉和量子态蒸馏，还在具有一维DPLSs的三端口有损耗系统中，对多种输入态演示了鲁棒W态生成。通过研究系统的损耗诱导子空间结构，本文分析有损耗系统中量子态演化的通用理论明确揭示了量子相干性、量子退相干与光子数减少之间的相互作用。通过调控损耗，所构建的DPLSs可用于精确控制耗散系统中的量子干涉，在量子态制备、量子逻辑操作及其他量子信息处理中具有潜在应用。
英文摘要
Quantum coherence, quantum decoherence, and photon number reduction are coexistent in linear lossy optical systems. However, how these three elements combine together to determine the evolution of the quantum light remains unclear. Here, based on singular value decomposition (SVD), we propose the theory of deterministic photon-loss subspace (DPLS) for quantum interferences in lossy systems. By performing an SVD of scattering matrices with singular values either 0 or 1, a series of completely lossy and lossless input modes are first defined. According to n_1,...,n_i photons in the first,..., i-th lossy modes, the Hilbert space of the input states can be decomposed into a set of orthogonal subspaces H_((n_1,...,n_i ))^in, i.e., deterministic photon-loss subspaces (DPLSs). When the concept of DPLS is established, the input state can be projected onto these DPLSs. In each DPLS, the photons in lossy modes will be completely dissipated, while those in lossless modes experience a unitary evolution. The output state is a statistical mixture of the evolved outcomes of all projections, since decoherence is a concurrent process. Then, based on the DPLS theory, we not only revisited Anti-HOM interference and the distillation of quantum states, but also demonstrate a robust W-state generation for various input states in a three-port lossy system with one-dimensional DPLSs. Through investigating the loss-induced subspace structure of the system, our general theory for analyzing quantum state evolution in lossy systems explicitly reveals the interplay among quantum coherence, quantum decoherence, and photon number reduction. By engineering the loss, the constructed DPLSs can be used to precisely control quantum interferences in dissipative systems, with potential applications in quantum state preparation, quantum logic operations, and other quantum information processes.
