  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.
