Conditional Mutual Information and Quantum Phase Transitions

Abstract

We investigate conditional mutual information as a diagnostic of quantum phase and quantum phase transitions. Using the QWZ and BHZ topological insulators, we demonstrate the divergence of the CMI across phase transitions and connect it to the quantum information theoretic understanding of entanglement entropy with the Fawzi-Renner recovery error bound. In the pure state we verify that the conditional mutual information I(A:C|B) and the mutual information I(A:C) approach each other. In the thermal mixed state we find that the conditional mutual information decays to zero and the Chern insulator approaches the maximally mixed quantum Markov chain, independently of phase. We further investigate the nature of conditional mutual information by defining new entanglement Hamiltonians H1=HABE+HAE⊗IB−IA⊗HBE and H2=HBCE+HABE−HBE−HABCE. The low-lying spectra and wave functions of these entanglement Hamiltonians reveal the dynamics of the CMI in terms of spatial correlations between the tripartite regions.