We show that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. If the squeezing parameter is less than or equal to 1, we demonstrate a quantitative relation between the squeezing parameter and the concurrence for the even and odd states. We prove that the even states generated from the initial state with all qubits being spin down, via the one-axis twisting Hamiltonian, are spin squeezed if and only if they are pairwise entangled. For the states generated via the one-axis twisting Hamiltonian with an external transverse field for any number of qubits greater than 1 or via the two-axis countertwisting Hamiltonian for any even number of qubits, the numerical results suggest that such states are spin squeezed if and only if they are pairwise entangled.We show that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. If the squeezing parameter is less than or equal to 1, we demonstrate a quantitative relation between the squeezing parameter and the concurrence for the even and odd states. We prove that the even states generated from the initial state with all qubits being spin down, via the one-axis twisting Hamiltonian, are spin squeezed if and only if they are pairwise entangled. For the states generated via the one-axis twisting Hamiltonian with an external transverse field for any number of qubits greater than 1 or via the two-axis countertwisting Hamiltonian for any even number of qubits, the numerical results suggest that such states are spin squeezed if and only if they are pairwise entangled.

arXiv:quant-ph/0302014Physical Review AJul 2, 2003228 citations

Quantum entanglement in multi-qubit systems

최정운

Jan 1, 20040 citations

Spin squeezing properties of an initial coherent state via a two-axis countertwisting Hamiltonian in the presence and absence of an external fleld

Ahmad Akhound, Mojtaba Jafarpour

We consider a four-qubit system, initially in a coherent state along the z-axis, and study its time dependence under the influence of the well-known two-axis countertwisting Hamiltonian. Analyzing the time dependence of the spin operators, we observe its squeezing properties, according to the criterion given by Kitagawa et al. We also perform similar calculations for the same Hamiltonian in the presence of an external fleld and compare its squeezing properties with that of the former. It is observed that the details of the squeezing properties are difierent in the two cases. Plots of the squeezing parameters as a function of time and the rotation angle for both cases are presented.We consider a four-qubit system, initially in a coherent state along the z-axis, and study its time dependence under the influence of the well-known two-axis countertwisting Hamiltonian. Analyzing the time dependence of the spin operators, we observe its squeezing properties, according to the criterion given by Kitagawa et al. We also perform similar calculations for the same Hamiltonian in the presence of an external fleld and compare its squeezing properties with that of the former. It is observed that the details of the squeezing properties are difierent in the two cases. Plots of the squeezing parameters as a function of time and the rotation angle for both cases are presented.

Journal of Physics Conference SeriesAug 1, 20084 citations

Scalable spin-nematic squeezing in multi-level dipole-interacting Rydberg atom arrays

Sakshi Bahamnia, Thomas Bilitewski

We study the generation of metrologically useful entanglement in a three-level (spin-1) system naturally realized in arrays of dipole-interacting Rydberg atoms confined in optical tweezers. In the spin-quadrupolar operator basis, the interaction Hamiltonian decomposes into effective SU(2) subspaces, within which quench dynamics from product initial states generate scalable spin-nematic squeezing. For symmetric interactions, we identify a mapping to effective one-axis twisting within bright and dark manifolds and demonstrate that the squeezing parameter scales as $ξ^{2}\propto N^{-2/3}$ ( $ξ^{2}\propto N^{-0.5}$ ) with system size for all-to-all (two-dimensional dipolar) couplings. In both cases the quantum Fisher information reaches $F_Q\propto N^{2}$ . For antisymmetric interactions supplemented by a microwave drive we find a distinct two-axis countertwisting mechanism. This results in squeezing $ξ^{2}\propto N^{-0.7}$ for all-to-all interactions and moderate squeezing for dipolar interactions in 2D. Our results constitute a first theoretical step beyond the well-studied qubit setting toward scalable entanglement generation in qudit systems with dipolar interactions, directly relevant to current Rydberg tweezer experiments.We study the generation of metrologically useful entanglement in a three-level (spin-1) system naturally realized in arrays of dipole-interacting Rydberg atoms confined in optical tweezers. In the spin-quadrupolar operator basis, the interaction Hamiltonian decomposes into effective SU(2) subspaces, within which quench dynamics from product initial states generate scalable spin-nematic squeezing. For symmetric interactions, we identify a mapping to effective one-axis twisting within bright and dark manifolds and demonstrate that the squeezing parameter scales as $ξ^{2}\propto N^{-2/3}$ ($ξ^{2}\propto N^{-0.5}$) with system size for all-to-all (two-dimensional dipolar) couplings. In both cases the quantum Fisher information reaches $F_Q\propto N^{2}$. For antisymmetric interactions supplemented by a microwave drive we find a distinct two-axis countertwisting mechanism. This results in squeezing $ξ^{2}\propto N^{-0.7}$ for all-to-all interactions and moderate squeezing for dipolar interactions in 2D. Our results constitute a first theoretical step beyond the well-studied qubit setting toward scalable entanglement generation in qudit systems with dipolar interactions, directly relevant to current Rydberg tweezer experiments.

quant-pharXiv:2605.00096May 4, 20260 citations

ξ^{2}\propto N^{-2/3}

(

ξ^{2}\propto N^{-0.5}

) with system size for all-to-all (two-dimensional dipolar) couplings. In both cases the quantum Fisher information reaches

F_Q\propto N^{2}

. For antisymmetric interactions supplemented by a microwave drive we find a distinct two-axis countertwisting mechanism. This results in squeezing

ξ^{2}\propto N^{-0.7}

for all-to-all interactions and moderate squeezing for dipolar interactions in 2D. Our results constitute a first theoretical step beyond the well-studied qubit setting toward scalable entanglement generation in qudit systems with dipolar interactions, directly relevant to current Rydberg tweezer experiments.