We present a one-dimensional tight-binding chain of two-level systems coupled only through common dissipative Markovian reservoirs. This quantum chain can demonstrate anomalous thermodynamic behavior contradicting Fourier law. Population dynamics of
individual systems of the chain is polynomial with the order determined by the initial state of the chain. The chain can simulate classically hard problems, such as multi-dimensional random walks.
We present an efficient and robust method for the reconstruction of photon number distributions by using solely thermal noise as a probe. The method uses a minimal number of pre-calibrated quantum devices, only one on/off single-photon detector is su
fficient. Feasibility of the method is demonstrated by the experimental inference of single-photon, thermal and two-photon states. The method is stable to experimental imperfections and provides a direct, user-friendly quantum diagnostics tool.
