The paper by Dakic, Vedral, and Brukner addresses the necessary and sufficient condition for the existence of non-zero quantum discord in bipartite states. Quantum discord is a measure of "non-classicality" in quantum correlations, which has been proposed as a key resource in quantum communication and computation tasks. The authors derive a simple and experimentally implementable condition for non-zero quantum discord, which involves checking the commutativity of certain operators. They also introduce a geometric measure of quantum discord, providing an explicit formula for two-qubit states. The paper applies these results to the DQC1 model, a quantum computing model that uses highly mixed states to perform tasks efficiently. The authors argue that quantum discord is unlikely to be the primary resource behind the speedup in DQC1, as the correlations in the output state are classical and can be efficiently evaluated on a classical computer. The paper concludes by discussing the limitations and extensions of their method to more complex systems.The paper by Dakic, Vedral, and Brukner addresses the necessary and sufficient condition for the existence of non-zero quantum discord in bipartite states. Quantum discord is a measure of "non-classicality" in quantum correlations, which has been proposed as a key resource in quantum communication and computation tasks. The authors derive a simple and experimentally implementable condition for non-zero quantum discord, which involves checking the commutativity of certain operators. They also introduce a geometric measure of quantum discord, providing an explicit formula for two-qubit states. The paper applies these results to the DQC1 model, a quantum computing model that uses highly mixed states to perform tasks efficiently. The authors argue that quantum discord is unlikely to be the primary resource behind the speedup in DQC1, as the correlations in the output state are classical and can be efficiently evaluated on a classical computer. The paper concludes by discussing the limitations and extensions of their method to more complex systems.