Quantum discord, as a measure of all quantum correlations, has been proposed as the key resource in certain quantum communication tasks and quantum computational models without containing much entanglement. Dakić et al. (Phys Rev Lett 105:190502, 2010) introduced a geometric measure of quantum discord (GMQD) and derived an explicit formula for any two-qubit state. Luo and Fu (Phys Rev A 82:034302, 2010) introduced another form of GMQD and derived an explicit formula for arbitrary state in a bipartite quantum system. However, the explicit analytical expression for any bipartite system was not given. In this work, we give out the explicit analytical expressions of the GMQD for a two-parameter class of states in a qubit–qutrit system and study its dynamics for the states under various dissipative channels in the first time. Our results show that all these dynamic evolutions do not lead to a sudden vanishing of GMQD. Quantum correlations vanish at an asymptotic time for local or multi-local dephasing, phase-flip, and depolarizing noise channels. However, it does not disappear even though t → ∞ for local trit-flip and local trit-phase-flip channels. Our results maybe provide some important information for the application of GMQD in hybrid qubit–qutrit systems in quantum information.
Quantum Information Processing – Springer Journals
Published: Jul 29, 2012
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