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.