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 was recently predicted that, in a composite quantum system exposed to dephasing noise, quantum coherence in a transversal reference basis can stay protected for an indefinite time. This can occur for a class of quantum states independently of the measure used to quantify coherence, and it 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, realizing 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 it highlights the natural resilience of quantum effects in complex systems.

Since the dawn of quantum theory, coherence has been attributed as a key to understand the weirdness of fundamental concepts such as, e.g., the wave-particle duality and the Stern-Gerlach experiment. Recently, based on a resource theory approach, the notion of quantum coherence was revisited and a plethora of coherence quantifiers was proposed. In this work, we address such issue employing the language of coherence orders developed by the NMR community. This allowed us to investigate the role played by different subspaces of the Hilbert-Schmidt space into physical processes and quantum protocols. We found some links between decoherence and each coherence order. Moreover, we propose a sufficient and straightforward method to testify the usefulness of a given state for quantum enhanced phase estimation, relying on a minimal set of elements belonging to the density matrix.