Generalized spin squeezing inequalities in $N$ qubit systems: theory and experiment

Details Generalized spin squeezing inequalities in $N$ qubit systems: theory and experiment Generalized spin squeezing inequalities in $N$ qubit systems: theory and experiment

2006-01-05

arxiv.org/abs/quant-ph/0601038v3

Phys. Rev. A 74, 052319 (2006)

Physics

Quantum Physics

Final version

Scientific paper

10.1103/PhysRevA.74.052319

We present detailed derivations, various improvements and application to concrete experimental data of spin squeezing inequalities formulated recently by some of us [Phys. Rev. Lett. {\bf 95}, 120502 (2005)]. These inequalities generalize the concept of the spin squeezing parameter, and provide necessary and sufficient conditions for genuine 2-, or 3- qubit entanglement for symmetric states, and sufficient entanglement condition for general $N$-qubit states. We apply our method to theoretical study of Dicke states, and, in particular, to $W$-states of $N$ qubits. Then, we analyze the recently experimentally generated 7- and 8-ion $W$-states [Nature {\bf 438}, 643 (2005)]. We also present some novel details concerning this experiment. Finally, we improve criteria for detection of genuine tripartite entanglement based on entanglement witnesses.

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