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Quantum discord, as a measure of all quantum correlations, has been proposedas the key resource in certain quantum communication tasks and quantumcomputational models without containing much entanglement. Daki\'{c}, Vedral,and Brukner [Phys. Rev. Lett. 105, 190502 (2010)] introduced a geometricmeasure of quantum discord (GMQD) and derived an explicit formula for anytwo-qubit state. Luo and Fu [Phys. Rev. A 82, 034302 (2010)] introduced anotherform of GMQD and derived an explicit formula for arbitrary state in a bipartitequantum system. However, the explicit analytical expression for any bipartitesystem was not given. In this work, we give out the explicit analyticalexpressions of the GMQD for a two-parameter class of states in a qubit-qutritsystem and study its dynamics for the states under various dissipative channelsin the first time. Our results show that all these dynamic evolutions do notlead to a sudden vanishing of GMQD. Quantum correlations vanish at anasymptotic time for local or multi-local dephasing, phase-flip, anddepolarizing noise channels. However, it does not disappear even though t --->$\infty$ for local trit-flip and local trit-phase-flip channels. Our resultsmaybe provide some important information for the application of GMQD in hybridqubit-qutrit systems in quantum information.

Geometric measure of quantum discord for a two-parameter class of states in a qubit-qutrit system under various dissipative channels