Quantum entanglement is one of the most important measures of quantum correlations. Using group-theoretical approach we found a family of four nine-parameter quantum states for the two-spin-1/2 Heisenberg system in an external magnetic field and with multiple components of Dzyaloshinsky-Moriya (DM) and Kaplan-Shekhtman- Entin-Wohlman-Aharony (KSEA) interactions. Exact analytical formulas are derived for the entanglement of formation for the quantum states found. In the proceeding, the family of found states and the structure of interactions in them are discussed.
The spin-1/2 XXZ chain in a uniform magnetic field at thermal equilibrium is considered. For this model, we give phase diagrams for the one-way quantum work deficit (thermal discord). The diagrams can contain regions with both stationary and variable (state-dependent) angles of optimal measurement. We also established a relationship between the behavior of optimal measurement angles near the boundaries separated different regions and Landau’s theory of phase transitions of the second and first kind. Namely, when crossing the boundary from a region with a stationary optimal measurement angle (0 or π/2) to the region with a variable angle of optimal measurement (0 < ϑ < π/2), quantum discord and one-way quantum work deficit experience a sudden change (“catastrophe”) in their behavior. The sudden change is accompanied by a splitting of the minimum characterizing stationary point of quantum correlation into two minima (i.e., bifurcation of the initial single minimum occurs). Such phenomena are analogous to phase transitions described within the Landau theory, or, more generally, by the mathematical formalism of catastrophe theory.
The one-way quantum work deficit, a measure of quantum correlation, exhibits the regions with the bimodal behavior of post-measurement entropy versus the measurement angle θ ε (0, π/2). Under certain conditions this can lead to the finite jumps Δν> 0 of optimal measurement angle ν from the endpoint 0 or π/2 to the interior minimum and vice versa. In turn, such sudden jumps lead to the fractures, i.e., non-analytical points on the dependencies of quantum correlation upon the state parameters. We examine a possibility to experimentally observe these phenomena on an example of three-component mixture consisting of one pair of Bell-diagonal states and a basis state orthogonal to the Bell ones. Observation of named effects, beyond their intrinsic interest, could demonstrate the experimental ability in controlling and manipulating the quantum states.