Quantum discord represents a correlation beyond classicality that could be useful for many quantum information tasks and therefore is viewed as a valuable quantum resource. Theoretically, whether or not a bipartite quantum state has a nonzero amount of quantum discord can be determined once its density matrix is given. Experimentally, however, it is not easy to perform a reliable tomography on the state, especially when considering the imperfection of devices and the high dimensionality of the system. Here, inspired by the so-called dimension witness, we propose a new approach using uncharacterized measurements to witness quantum discord of an unknown bipartite state within an arbitrary-dimension system. Furthermore, $2\times 2$ measurements are sufficient for any bipartite state of arbitrarily large dimension. For any two-qubit state, we show that the maximum of the witness happens when one performs mutually orthogonal basis measurements on each qubit. Moreover, the witness value decreases linearly in response to the errors, which indicates its nonsensitivity to device imperfections and experimental feasibility.

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• Quantum correlations in quantum information
• Quantum correlations, foundations & formalism
• Quantum discord
• Quantum information theory
• Quantum measurements