Measuring quantum discord using the most distinguishable steered states

Abstract

Any two-qubit state can be represented, geometrically, as an ellipsoid with a certain size and a center located within the Bloch sphere of one of the qubits. Points of this ellipsoid represent the post-measurement states when the other qubit is measured. Based on the most demolition concept in the definition of quantum discord, we study the amount of demolition when the two post-measurement states, represented as two points on the steering ellipsoid, have the most distinguishability. We use trace distance as a measure of distinguishability and obtain the maximum distinguishability for some classes of states, analytically. Using the optimum measurement that gives the most distinguishable steered states, we extract quantum correlation of the state and compare the result with the quantum discord. It is shown that there are some important classes of states for which the most demolition happens exactly at the most distinguished steered points. Correlations gathered from the most distinguished post-measurement states provide a faithful and tight upper bound touching the quantum discord in most of the cases.

8 pages, 7 figures

References in corpus (11)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Quantifying Einstein-Podolsky-Rosen steering
• Quantum discord for general two--qubit states: Analytical progress
• Optimal measurements to access classical correlations of two-qubit states
• Quantum steering ellipsoids, extremal physical states and monogamy
• Quantum correlations of two-qubit states with one maximally mixed marginal
• Role of thermal noise in tripartite quantum steering
• Einstein-Podolsky-Rosen Steering and Quantum Steering Ellipsoids: Optimal Two-Qubit States and Projective Measurements
• Effect of Local Channels on Quantum Steering Ellipsoids
• Quantum discord for the general two-qubit case