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

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

2011-12-20

arxiv.org/abs/1112.4693v4

Physics

Quantum Physics

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

Scientific paper

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 $\rho^{T_B}_{AB}$, 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.

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