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In conventional experiments, quantum systems are interrogated by measurement devices which destroy quantum coherence. We theoretically develop the new subject of 'chromatic interferometry' by going beyond the usual paradigm: we deliberately entangle experimental samples with lab apparatuses and perform coherent quantum operations on the joint system to extract hidden correlations. This enables a new and powerful method of high-resolution imaging for multi-wavelength sources, which has been experimentally realized by the group of Jian-Wei Pan. The method has applications ranging from astrophysics to microscopy.More broadly, we will discuss a quantum information-theoretic framework to study experiments where apparatuses can be entangled with experimental samples, and quantum coherence is maintained thereafter. It can be proved that for several 'model' experiments, there is an exponential savings in resources if the experimentalist can entangle apparatuses with experimental samples.