Characterizing nonclassical correlation using affinity

Abstract

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 × n dimensional arbitrary mixed state and a closed formula of proposed version of geometric discord for 2 × n dimensional mixed state are obtained. Finally, as are illustrations, we have studied the quantum correlation of Bell diagonal state, isotropic and Werner states.

Affinity-based geometric discord and quantum speed limits of its creation and decay

“…where A(ρ, σ) = Tr √ ρ √ σ is the affinity between the states ρ and σ [47,51] and d A (ρ, σ) = 1 − A(ρ, σ) is a affinityinduced metric. In recent times, the usefulness of affinity in characterization of quantum correlation of bipartite state [52], bilocal state [53] and quantum coherence [54,55] is also demonstrated. A similar quantum correlation measure is characterized using Hellinger distance [50].…”

Text-based multi-dimensional medical images retrieval according to the features-usage correlation

“…Different approaches are used for affinity computation, ranging from mathematical computation (such as in [22]), or feedback through medical social network (e.g., in [17,23]), to using data mining techniques such as the Random forest and Gaussian process regression algorithms [24].…”

Measurement-induced nonlocality based on affinity

“…Further, it is easy to show that the above-defined metric satisfies all the axioms of a valid distance measure in state space. This metric is also useful in quantifications in quantum resources, such as entanglement [30], nonclassical correlation [32] and quantum coherence. To define affinity-based MIN, we set α=1/2.…”