Effect of Local Channels on Quantum Steering Ellipsoids

Abstract

The effect of a local trace-preserving single-qubit channel on a two-qubit state is investigated in the picture of the quantum steering ellipsoids (QSE). The phenomenon of locally increased quantum correlation is visualized in this picture. We strictly prove that a $B$-side two-qubit discordant state can be locally prepared from a classical state by a trace-preserving channel on qubit $B$ if and only if its QSE of $B$ is a non-radial line segment. For states with higer-dimensional QSEs, the phenomenon of locally increased quantum correlation generally happens when the shape of the QSE is like a baguette. Based on this observation, we find a class of entangled states whose quantum discord can be increased by the local amplitude damping channel. Further, We find that the local quantum channel does not increase the size of QSEs of either qubit $A$ or qubit $B$, for the needle-shape QSE states, as well as the Bell diagonal states with higher-dimensional QSE.

arXiv comment6 pages, 2 figures. Comments are welcome

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• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Experimental verification of the steering ellipsoid zoo via two-qubit states
• Conditional states and entropy in qudit-qubit systems
• Measuring quantum discord using the most distinguishable steered states
• Protection of quantum steering ellipsoids in non-Markovian environments