Quantum Matter Seminar

Studies of entanglement in the ground states of locally interacting many-body quantum systems have provided insights into the relation between spatial correlations, low-energy spectral properties, and computational resource requirements. However, at finite temperatures, relations between entanglement, physical correlations, and computational resources, are less clear. For example, it was only recently demonstrated that Gibbs state are exactly separable above a finite temperature. In this talk I will first show how the quantum resources required to prepare a mixed state are related to the private information, a central quantity in quantum cryptography. Then I will relate the private information in thermal states to their linear response, and to standard spatial correlation functions. Using these results, I will show how techniques from quantum statistical mechanics can be leveraged to lower bound the resources necessary to approximate equilibrium states and, moreover, that these resources depend sensitively on symmetries of the thermal ensemble. arXiv:2502.13218 + upcoming work, SJG & Max McGinley.