Wave-particle duality, the cornerstone of quantum mechanics, illustrates essential trade-offs between two complementary aspects of quantum systems. Captured by Bohr's complementarity principle, the wave-particle duality relation indicates that perfect path discrimination in a multipath interferometer obliterates interference patterns and vice versa. In this work, from the perspective of coherence resource manipulation, we uncover a novel duality relation between quantum coherence and distinguishability in ensembles of mutually orthogonal pure states. We demonstrate the sum of `co-bits', coherence preserved after discrimination, and classical bits, distinguishability extracted through perfect discrimination is bounded. One cannot simultaneously extract all classical information and preserve coherence. Such duality relation exposes an inherent trade-off between quantum coherence and classical distinguishability resources. Our findings offer a fresh perspective and advance our understanding of the intrinsic complementary relationship between quantum and classical resources.

翻译：波粒二象性是量子力学的基石，揭示了量子系统两个互补方面之间的本质权衡。依据玻尔互补原理，波粒二象性关系表明：在多路径干涉仪中实现完美路径区分将消除干涉条纹，反之亦然。本研究从相干性资源操控的视角，揭示了相互正交纯态系综中量子相干性与可区分性之间一种新颖的二象性关系。我们证明，"相干比特"（经区分后保留的相干性）与经典比特（通过完美区分提取的可区分性）之和存在边界约束——无法同时提取全部经典信息并保持相干性。这种二象性关系揭示了量子相干性与经典可区分性资源之间的内在权衡。我们的发现为理解量子与经典资源之间的固有互补关系提供了全新视角，并深化了相关认识。