# Berlin 2014 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 50: Quantum information: Concepts and methods III

### Q 50.4: Vortrag

### Donnerstag, 20. März 2014, 17:15–17:30, Kinosaal

**Generalized squeezing inequalities, entanglement and its depth** — Giuseppe Vitagliano^{1}, Zoltan Zimboras^{1}, and •Geza Toth^{1,2,3} — ^{1}Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain — ^{2}IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain — ^{3}Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary

We present a general method to derive sets of *SU*(*d*) squeezing inequalities
for *d*-level particle systems. In [1] we presented a set of necessary separability
criteria based on the first and the “modified” second moments of collective
operators. Considering the total spin components as collective operators,
these conditions yield the so-called generalized spin squeezing
inequalities [2], which outperform traditional methods for detecting
entanglement in spin ensembles (like the criterion of Ref. [3]). Here we
present similar entanglement conditions based on the first and modified second moments of the collective *SU*(*d*)-generators. From these we define a parameter that is suitable to detect entangled states that might be useful for quantum metrology and even states that are biseparable with respect to
all possible bipartitions. We also present a criterion for detecting the entanglement depth, i.e., whether the state is *k*-producible or not.

[1] GV, P. Hyllus, I.L. Egusquiza, and G. Tóth, PRL **107**, 240502

[2] GV, I. Apellaniz, I.L. Egusquiza, and G. Tóth, arXiv:1310.2269

[3] A. Sørensen, L.-M. Duan, J.I. Cirac, P. Zoller, Nature **409**, 63 (2001).