Thermal quantum coherence and correlations in a spin-1 Heisenberg model

The l1 norm and the relative entropy have been recently proposed as a information measure of quantum coherence (Baumgratz et al., 2014). Here their properties are studied for the thermal quantum state in a spin-1 Heisenberg model with various couplings, external magnetic fields, and temperatures as well. Quantum correlations quantified via quantum discord, quantum deficit, and the generalized negativity are simulated for reference. It is shown that quantum coherence, discord, and deficit are nonzero whereas the negativity is zero in some ranges of model parameters and temperature. Moreover, quantum coherence, discord, and deficit are more robust than the negativity against temperature and magnetic field. However, all those quantities at lower temperatures behave similarly. Remarkably, quantum deficit exhibits double sudden changes under suitable conditions while quantum coherence, discord, and entanglement do not display such a phenomenon. The hierarchy of two coherence measures and the hierarchy of quantum discord and deficit are discussed. Those are useful for understanding quantumness in high-dimensional mixed states and quantum tasks.