Characterizing nonclassical correlation using affinity

Geometric discord (GD), a measure of quantumness of bipartite system, captures minimal nonlocal effects of a quantum state due to locally invariant von Neumann projective measurements. The original version of GD is suffered by local ancilla problem. In this article, we propose a new version of geometric discord using affinity. This quantity satisfies all the necessary criteria of a good measure of quantum correlation for bipartite system and resolves local ancilla problem. We evaluate analytically the proposed discord for both pure and mixed states. For an arbitrary pure state, it is shown that affinity-based geometric discord is same as geometric measure of entanglement. Further, a lower bound of this measure for $m\times n$-dimensional arbitrary mixed state and a closed formula of proposed version of geometric discord for $2\times n$-dimensional mixed state are obtained. Finally, as are illustrations, we have studied the quantum correlation of Bell diagonal state, isotropic and Werner states.