In quantum science we often simplify our analyses by treating quantum systems as two-level qubits, and by assuming that the decoherence events of two or more unentangled qubits are uncorrelated from each other. For example, both of these assumptions are central tenets of circuit-based quantum error correction protocols. However, in experiments these assumptions regularly break down, offering both challenges and opportunities. In this talk I will present two concrete experimental examples in which a detailed understanding of the multi-level nature of decoherence in a specific quantum system and measurements of shot-to-shot classical correlations in the “decoherence” of qubits can be harnessed to enable new capabilities and to achieve unprecedented levels of performance. The first example will be recent precision measurements we have performed with a new kind of spatially multiplexed strontium optical lattice clock. The second example will be a detailed experimental study of spin-phonon relaxation in nitrogen vacancy (NV) centers in diamond, and the experimental demonstration of spatiotemporal magnetic field correlation measurements with pairs of NV centers. Time permitting, I will present a third example of a theoretical proposal to take advantage of the details of the level structure of alkaline-earth atoms to significantly relax the error correction threshold for quantum computation with neutral atom qubits.