Inequalities Detecting Quantum Entanglement for 2 ⊗ d Systems
Ming-Jing Zhao, Teng Ma, Shao-Ming Fei,and Zhi-Xi Wang
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Submission date: 03. Sep. 2011
published in: Physical review / A, 83 (2011) 5, art-no. 052120
DOI number (of the published article): 10.1103/PhysRevA.83.052120
PACS-Numbers: 03.65.Ud, 03.67.Mn
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We present a set of inequalities for detecting quantum entanglement of 2 ⊗ d quantum states. For 2 ⊗ 2 and 2 ⊗ 3 systems, the inequalities give rise to sufficient and necessary separability conditions for both pure and mixed states. For the case of d > 3, these inequalities are necessary conditions for separability, which detect all entangled states that are not positive under partial transposition and even some entangled states with positive partial transposition. These inequalities are given by mean values of local observables and present an experimental way of detecting the quantum entanglement of 2 ⊗ d quantum states and even multi-qubit pure states.