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

J. K. Korbicz·O. Gühne·M. Lewenstein·H. Haeffner·C. F. Roos·R. Blatt
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Abstract

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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J. K. Korbicz, O. Gühne, M. Lewenstein, H. Haeffner, C. F. Roos, R. Blatt. 2006-01-05. Generalized spin squeezing inequalities in $N$ qubit systems: theory and experiment. https://doi.org/10.1103/physreva.74.052319

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