Quantum coherence is the most fundamental of all quantum quantifiers, underlying other well-known quantities such as entanglement. It can be distributed in a multipartite system in various ways—for example, in a bipartite system it can exist within subsystems (local coherence) or collectively between the subsystems (global coherence), and exhibits a trade-off relation. In this paper, we experimentally verify these coherence trade-off relations in adiabatically evolved nuclear spin systems using an NMR spectrometer. We study the full set of coherence trade-off relations between the original state, the bipartite product state, the tripartite product state, and the decohered product state. We also experimentally verify the monogamy inequality and show that both the quantum systems are polygamous during the evolution. We find that the properties of the state in terms of coherence and monogamy are equivalent. This illustrates the utility of using coherence as a characterization tool for quantum states.

量子相干性是所有量子量词中最基本的，是其他众所周知的量（如纠缠）的基础。它可以以多种方式分布在多方系统中——例如，在一个二方系统中，它可以存在于子系统内（局部一致性），也可以存在于子系统之间（全局一致性），并表现出一种权衡关系。在本文中，我们使用 NMR 光谱仪通过实验验证了绝热演化核自旋系统中的这些相干权衡关系。我们研究了原始状态、二分乘积状态、三分乘积状态和去相干乘积状态之间的全套相干权衡关系。我们还通过实验验证了一夫一妻制不等式，并表明两个量子系统在进化过程中都是一夫多妻的。我们发现国家在一致性和一夫一妻制方面的属性是等价的。这说明了使用相干性作为量子态表征工具的实用性。