  We address the issue of reducing the resource required to compute
information-theoretic quantum correlation measures like quantum discord and
quantum work deficit in two qubits and higher dimensional systems. We show that
determination of the quantum correlation measure is possible even if we utilize
a restricted set of local measurements. We find that the determination allows
us to obtain a closed form of quantum discord and quantum work deficit for
several classes of states, with a low error. We show that the computational
error caused by the constraint over the complete set of local measurements
reduces fast with an increase in the size of the restricted set, implying
usefulness of constrained optimization, especially with the increase of
dimensions. We perform quantitative analysis to investigate how the error
scales with the system size, taking into account a set of plausible
constructions of the constrained set. Carrying out a comparative study, we show
that the resource required to optimize quantum work deficit is usually higher
than that required for quantum discord. We also demonstrate that minimization
of quantum discord and quantum work deficit is easier in the case of two-qubit
mixed states of fixed ranks and with positive partial transpose in comparison
to the corresponding states having non-positive partial transpose. Applying the
methodology to quantum spin models, we show that the constrained optimization
can be used with advantage in analyzing such systems in quantum
information-theoretic language. For bound entangled states, we show that the
error is significantly low when the measurements correspond to the spin
observables along the three Cartesian coordinates, and thereby we obtain
expressions of quantum discord and quantum work deficit for these bound
entangled states.
