Quantum coherence, present whenever a quantum system exists in a superposition of , marks one of the fundamental departures from classical physics. Quantum coherence has recently been investigated rigorously within a resource-theoretic formalism. However, the finer-grained notion of , which explicitly takes into account the number of superposed classical states, has remained relatively unexplored. A comprehensive analysis of multi-level coherence, which acts as the single-party analogue to multi-partite entanglement, is essential for understanding natural quantum processes as well as for gauging the performance of quantum technologies. Here we develop the theoretical and experimental groundwork for characterizing and quantifying multilevel coherence. We further verify and lower-bound the robustness of multilevel coherence by performing a phase discrimination task, which is implemented experimentally with four-level quantum probes in a photonic setup. Our results contribute to understanding the operational relevance of genuine multilevel coherence, also by demonstrating the key role it plays in enhanced phase discrimination—a primitive for quantum communication and metrology—and suggest new ways to reliably and effectively test the quantum behaviour of physical systems.

中文翻译：

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多级量子相干的认证和量化

每当量子系统以叠加存在时，就会出现量子相干，这是与经典物理学的根本偏离之一。最近在资源理论形式主义中对量子相干性进行了严格的研究。但是，的细粒度概念明确考虑了叠加的古典状态的数量，至今仍未得到充分研究。多级相干性的全面分析是多方纠缠的单方模拟，对于理解自然量子过程以及衡量量子技术的性能至关重要。在这里，我们为表征和量化多级连贯性发展了理论和实验基础。我们通过执行相位区分任务进一步验证和降低多级相干性的鲁棒性，该任务是在光子设置中用四级量子探针通过实验实现的。我们的结果还通过证明它在增强的相位鉴别中（量子通信和计量学的原始方法）中发挥的关键作用，有助于理解真正的多级相干的操作相关性，并提出了可靠和有效地测试物理系统的量子行为的新方法。