Quantum discord Q is a function of density matrix elements. The domain of such a function in the case of two-qubit system with X density matrix may consist of three subdomains at most: two ones where the quantum discord is expressed in closed analyti
cal forms (Q_{pi/2} and Q_0) and an intermediate subdomain for which, to extract the quantum discord Q_theta, it is required to solve in general numerically a one-dimensional minimization problem to find the optimal measurement angle thetain(0,pi/2). Hence the quantum discord is given by a piecewise-analytic-numerical formula Q=min{Q_{pi/2}, Q_theta, Q_0}. Equations for determining the boundaries between these subdomains are obtained. The boundaries consist of bifurcation points. The Q_{theta} subdomains are discovered in the generalized Horodecki states, in the dynamical phase flip channel model, in the anisotropic spin systems at thermal equilibrium, in the heteronuclear dimers in an external magnetic field. We found that transitions between Q_{theta} subdomain and Q_{pi/2} and Q_0 ones occur suddenly but continuously and smoothly, i.e., nonanalyticity is hidden and can be observed in higher derivatives of discord function.
Quantum discord is a function of density-matrix elements (and through them, e.~g., of temperature, applied fields, time, and so forth). The domain of such a function in the case of two-qubit system with X or centrosymmetric (CS) density matrix can
consist at most of three subdomains: two ones, where the quantum discord is expressed in closed analytical forms (Q_0 and Q_{pi/2}), and an intermediate subdomain in which for determining the quantum discord Q_theta it is required to solve numerically a one-dimensional minimization problem to find the optimal measurement angle thetain(0,pi/2). Exact equations for determining the boundaries between these subdomains are obtained and solved for a number of models. The Q_theta subdomains are discovered in the anisotropic spin dimers in external field. On the other hand, coinciding boundaries and therefore sudden transitions between optimal measurement angles theta=pi/2 and theta=0 are observed in dynamics of spin currying particles in closed nanopore and also in phase flip channels. In latter cases the solutions are entirely analytical.
