Measuring geometric quantum discord using one bit of quantum information

We describe an efficient DQC1 (deterministic quantum computation with one quantum qubit) algorithm to quantify the amount of geometric quantum discord present in the output state of a DQC1 computation. DQC1 is a model of computation that utilizes separable states to solve a problem with no known efficient classical algorithm and is known to contain quantum correlations as measured by the discord. For the general case of a (1 + n)-qubit DQC1 state we provide an analytical expression for the geometric quantum discord and find that its typical (and maximum) value decreases exponentially with n. This is in contrast to the standard quantum discord whose value for typical DQC1 states is known to be independent of n. We experimentally demonstrate the proposed algorithm on a four-qubit liquid-state nuclear magnetic resonance quantum information processor. In the special case of a two-qubit DQC1 model, we also provide an expression for the quantum discord that only requires the outcome of the DQC1 algorithm.