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

2011/12/20 by Jing-Ling Chen, Jing‐Ling Chen, Chen, Jing-Ling +9
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.1112.4693

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

openalex publication_date 2011/12/20 · arxiv created 2012/01/28 · arxiv updated 2012/01/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We propose a sufficient criterion S=λ1+λ2-(λ1-λ2)2<0 to detect Einstein-Podolsky-Rosen steering for arbitrary two-qubit density matrix ρAB. Here λ1,λ2 are respectively the minimal and the second minimal eigenvalues of ρTBAB, which is the partial transpose of ρAB. 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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