Spin squeezing and entanglement

By Géza Tóth, Christian Knapp, Otfried Gühne, Hans J. Briegel. 2008

173 citations recorded by the source corpus.

What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized-spin-squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular-momentum components ${J}_{k}$. They can be used for the experimental detection of entanglement in a system of spin-$\frac{1}{2}$ particles in which the spins cannot be individually addressed. We present various sets of inequalities that can detect all entangled states that can be detected based on the knowledge of (i) the mean values and variances of ${J}_{k}$ in three orthogonal directions, or (ii) the variances of ${J}_{k}$ in three orthogonal directions, or (iii) the mean values of ${J}_{k}^{2}$ in three orthogonal directions, or (iv) the mean values and variances of ${J}_{k}$ in arbitrary directions. We compare our inequalities to known spin-squeezing entanglement criteria and discuss to which extent spin squeezing is related to entanglement in the reduced two-qubit states. Finally, we apply our criteria for the detection of entanglement in spin models, showing that they can be used to detect bound entanglement in these systems.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/f41c4aee63e241ff832eb4f49e83623232e2cc1c

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum spin squeezing (2010, methodology): “Inspired by Töh’s discussions [28, 195, 196], we will give slightly different definitions for ξ(2) R′ and ξ 2 D, and the new definitions provide us a simple way to determine whether a state is spin squeezed.”
Quantum-enhanced measurements without entanglement (2017, background): “…Holland and Burnett, 1993; Kacprowicz et al., 2010; Kitagawa and Ueda, 1993; Korbicz et al., 2005; Pezzè and Smerzi, 2009; Sanders and Milburn, 1995; Sørensen et al., 2001; Tóth et al., 2009; Uys and Meystre, 2007; Wang and Sanders, 2003; Wineland et al., 1994; Yurke, 1986; Yurke et al., 1986)).”
Quantum metrology with nonclassical states of atomic ensembles (2016, background): “The inequalities (48b)-(48d) have been introduced by Tóth et al. (2007, 2009).”
Entanglement certification from theory to experiment (2018, background): “As a generalization, a full set of spin-squeezing inequalities, which have the geometrical shape of a closed convex polytope and define a more general spin-squeezing quantifier, have been derived for spin12 ensembles [280, 281] and later generalised to all higher spin-j ensembles and also to su(d) o”