In the fields of computing and communications, quantum supremacy is well known. Quantum sensing can improve resolution, sensitivity, and accuracy of imaging, detection, and metrology. The question is, does quantum sensing have the so-called quantum supremacy, i.e., can it accomplish certain tasks that classical methods cannot? There are studies indicating that the answer may be positive. For example, Aharonov et al found that using quantum measurements, certain physical experiments can be exponentially accelerated. Our study also shows that quantum probes can probe the thermodynamics of environmental systems in the complex plane by using the intrinsic complex phase factors brought about by quantum evolution. In addition, we can select two different effects, namely, the probe-driven evolution of the environment or the environment-driven evolution of the probe, by preparing the initial state of the probe and selecting a certain measurement basis, so that we can detect any type of quantum correlations and realize the exponential expansion of the accessible correlations in an environment. Future research may reveal more aspects of quantum supremacy in detection applications.