LAUSR

For the XXZ subclass of symmetric two-qubit X states, we study the behavior of quantum conditional entropy $$S_{cond}$$Scond as a function of measurement angle $$\theta \in [0,\pi /2]$$θ∈[0,π/2]. Numerical calculations show that the function $$S_{cond}(\theta )$$Scond(θ) for X states can have at most one local extremum in the open interval from zero to $$\pi /2$$π/2 (unimodality property). If the extremum is a minimum, the quantum discord displays region with variable (state-dependent) optimal measurement angle $$\theta ^*$$θ∗. Such $$\theta $$θ-regions (phases, fractions) are very tiny in the space of X-state parameters. We also discover the cases when the conditional entropy has a local maximum inside the interval $$(0,\pi /2)$$(0,π/2). It is remarkable that the maxima exist in surprisingly wide regions, and the boundaries for such regions are defined by the same bifurcation conditions as for those with a minimum.