Effect of Local Channels on Quantum Steering Ellipsoids

TL;DR

This paper explores how local quantum channels affect quantum steering ellipsoids, revealing conditions under which quantum correlations can be increased and identifying specific state classes where this occurs.

Contribution

It provides a strict proof linking QSE shape to the ability to locally increase quantum discord, and identifies classes of states affected by local amplitude damping channels.

Findings

B-side discordant states can be prepared from classical states via local channels if QSE is a non-radial line segment.

Locally increased quantum correlation occurs when QSE resembles a baguette shape.

Local channels do not increase QSE size for needle-shape and certain Bell diagonal states.

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.