  The ability to live in coherent superpositions is a signature trait of
quantum systems and constitutes an irreplaceable resource for quantum-enhanced
technologies. However, decoherence effects usually destroy quantum
superpositions. It has been recently predicted that, in a composite quantum
system exposed to dephasing noise, quantum coherence in a transversal reference
basis can stay protected for indefinite time. This can occur for a class of
quantum states independently of the measure used to quantify coherence, and
requires no control on the system during the dynamics. Here, such an invariant
coherence phenomenon is observed experimentally in two different setups based
on nuclear magnetic resonance at room temperature, realising an effective
quantum simulator of two- and four-qubit spin systems. Our study further
reveals a novel interplay between coherence and various forms of correlations,
and highlights the natural resilience of quantum effects in complex systems.
