表征与定制多模参量下转换中的空间关联
Characterising and Tailoring Spatial Correlations in Multi-Mode Parametric Downconversion
AI总结：
该研究形式化纳入产生与测量系统的 JTMA 描述，并提出基于 $2Dπ$ 相位阶跃扫描的高效重建方法，以定制高维纠缠态并优化预示效率。
摘要：
在位置-动量自由度（DoFs）上纠缠的光子，是 Einstein-Podolsky-Rosen 佯谬的优雅体现，同时也增强了面向通信、成像和计算的量子技术。参量下转换所产生光子的多模特性，激发了新一代高维纠缠实验，其范围从完整的量子态隐形传态到奇异的多体纠缠。然而，由于探测器技术的限制，对底层位置-动量态进行精确表征是众所周知的难题，导致重建缓慢、不准确且充满噪声。此外，所生成双光子态的理论模型往往忽略测量系统的重要性，从而造成理论与实验之间的差异。在此，我们形式化地描述了空间域中的双光子波函数，称之为收集的联合横向动量振幅（JTMA），该描述同时纳入了所涉及的产生系统和测量系统。随后，我们提出并演示了一种实用且高效的方法，利用一种被称为 $2Dπ$ 测量的简单相位阶跃扫描，来精确重建收集的 JTMA。最后，我们讨论了对收集的 JTMA 的精确认识如何使我们能够生成定制的高维纠缠态，从而最大化形成纠缠度或纠缠维数等离散变量纠缠度量，并优化光子预示效率等关键实验参数。通过准确且高效地表征光子位置-动量纠缠，我们的结果释放了其在离散变量量子信息科学中的全部潜力，并为未来基于多模纠缠的量子技术奠定了基础。
英文摘要：
Photons entangled in their position-momentum degrees of freedom (DoFs) serve as an elegant manifestation of the Einstein-Podolsky-Rosen paradox, while also enhancing quantum technologies for communication, imaging, and computation. The multi-mode nature of photons generated in parametric downconversion has inspired a new generation of experiments on high-dimensional entanglement, ranging from complete quantum state teleportation to exotic multi-partite entanglement. However, precise characterisation of the underlying position-momentum state is notoriously difficult due to limitations in detector technology, resulting in a slow and inaccurate reconstruction riddled with noise. Furthermore, theoretical models for the generated two-photon state often forgo the importance of the measurement system, resulting in a discrepancy between theory and experiment. Here we formalise a description of the two-photon wavefunction in the spatial domain, referred to as the collected joint-transverse-momentum-amplitude (JTMA), which incorporates both the generation and measurement system involved. We go on to propose and demonstrate a practical and efficient method to accurately reconstruct the collected JTMA using a simple phase-step scan known as the $2Dπ$-measurement. Finally, we discuss how precise knowledge of the collected JTMA enables us to generate tailored high-dimensional entangled states that maximise discrete-variable entanglement measures such as entanglement-of-formation or entanglement dimensionality, and optimise critical experimental parameters such as photon heralding efficiency. By accurately and efficiently characterising photonic position-momentum entanglement, our results unlock its full potential for discrete-variable quantum information science and lay the groundwork for future quantum technologies based on multi-mode entanglement.
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