Measuring geometric quantum discord using DQC1

DQC1 is a model of quantum computation that utilizes a single qubit accompanied by a register of completely mixed states. While this model is able to outperform current classical methods without substantial entanglement, it does contain non-classical correlations as measured by the quantum discord. We describe an efficient algorithm to experimentally measure a near relative of the quantum discord, the geometric quantum discord, of a DQC1-state. We provide an analytical expression that indicates the geometric quantum discord of a $(1+n)$-qubit DQC1-state decreases exponentially with $n$. This is in contrast to the quantum discord, which is independent of $n$ for the same state. In addition, we present experimental results using a four-qubit liquid-state nuclear magnetic resonance quantum information processor.