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

Abstract

We propose a sufficient criterion ${S}=λ_1+λ_2-(λ_1-λ_2)^2<0$ to detect Einstein-Podolsky-Rosen steering for arbitrary two-qubit density matrix $ρ_{AB}$. Here $λ_1,λ_2$ are respectively the minimal and the second minimal eigenvalues of $ρ^{T_B}_{AB}$, which is the partial transpose of $ρ_{AB}$. 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