Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems

Details Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems

2011-05-24

arxiv.org/abs/1105.4668v1

Phys. Rev. A 83 (2011) 052120

Physics

Quantum Physics

6 pages

Scientific paper

10.1103/PhysRevA.83.052120

We present a set of inequalities for detecting quantum entanglement of $2\otimes d$ quantum states. For $2\otimes 2$ and $2\otimes 3$ 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 $2\otimes d$ quantum states and even multi-qubit pure states.

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