Einstein-Podolsky-Rosen Steerability Criterion for Two-Qubit Density Matrices

Abstract

We propose a sufficient criterion $S={\lambda }_1+{\lambda }_2-({\lambda }_1-{\lambda }_2{)}^2<0$ to detect Einstein-Podolsky-Rosen steering for arbitrary two-qubit density matrix ${\rho }_{AB}$. Here ${\lambda }_1,{\lambda }_2$ are respectively the minimal and the second minimal eigenvalues of ${\rho }_{AB}^{T_B}$, which is the partial transpose of ${\rho }_{AB}$. By investigating several typical two-qubit states such as the isotropic state, Bell-diagonal state, maximally entangled mixed state, etc., we show this criterion works efficiently and can make reasonable predictions for steerability. We also present a mixed state of which steerability always exists, and compare the result with the violation of steering inequalities.

4 pages, 3 figure. 3 figures are added. Comments are welcome

Cited by in corpus (1)

• Steering Bell-diagonal states