Characterizing nonclassical correlation using affinity

Abstract

Geometric discord, a measure of quantumness of bipartite system, captures minimal nonlocal effects of a quantum state due to locally invariant von Neumann projective measurements. Original version of this measure is suffered by the local ancilla problem. In this article, we propose a new version of geometric discord using affinity. This quantity satisfies all criteria of a good measure of quantum correlation of the bipartite system and resolves local ancilla problem of Hilbert-Schmidt norm based discord. We evaluate analytically the proposed quantity for both pure and mixed states. For an arbitrary pure state, it is shown that affinity based geometric discord equal to geometric measure of entanglement. Further, we obtain 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 is obtained. Finally, as an illustration, we have studied the nonlocality of Bell diagonal state, isotropic and Werner states.

13 pages, 1 figure, Comments are welcome

References in corpus (11)

• Quantum discord and the power of one qubit
• Necessary and sufficient condition for non-zero quantum discord
• Interpreting quantum discord through quantum state merging
• Operational interpretations of quantum discord
• Quantum discord for general two--qubit states: Analytical progress
• Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics
• Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling
• Universal freezing of quantum correlations within the geometric approach
• Unifying approach to the quantification of bipartite correlations by Bures distance
• Hellinger distance as a measure of Gaussian discord
• Fidelity based Measurement Induced Nonlocality and its dynamics in Quantum noisy channels