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Chinese Physics Letters

Spin Squeezing and Entanglement of Many-Particle Spin-Half States

Dong Yan, Xiaoguang Wang, Ling-An Wu

Published Jan 27, 2005• 11 citations
Publisher

Abstract

In many-particle spin-half systems with exchange symmetry, we find that the spin squeezing is related to two types of entanglement, the bipartite and the pairwise entanglement. A quantitative relationship is revealed for the spin squeezing parameter, the tangle, and the concurrence. We find that a class of states is spin squeezed if the pairwise entanglement is stronger than the bipartite entanglement.

DOI
10.1088/0256-307x/22/2/002

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In many-particle spin-half systems with exchange symmetry, we find that the spin squeezing is related to two types of entanglement, the bipartite and the pairwise entanglement. A quantitative relationship is revealed for the spin squeezing parameter, the tangle, and the concurrence. We find that a class of states is spin squeezed if the pairwise entanglement is stronger than the bipartite entanglement.
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 study entanglement and squeezing of a cluster of spin systems under the influence of the two-axis countertwisting Hamiltonian. The squeezing parameters given by Wineland et al and also by Kitagawa et al. are chosen as the criteria of spin squeezing. The criterion of pairwise entanglement is chosen to be the concurrence and that of the bipartite entanglement the linear entropy. We also define a new squeezing parameter η, which plays a direct role in the investigation of the relationship between squeezing and entanglement. We observe that if the system is squeezed according to the Wineland’s criterion, it is squeezed according to the Kitagawa’s also, but the reverse is not always true. Moreover, if the system is squeezed according to Kitagawa’s criterion, it is pairwise entangled simultaneously and vice versa. It is also observed that the entropy is a linear function of the parameter η2.
Coherent and squeezed photon states have attracted a lot attetion in long time ago, since these states can generate in laboratory. These states are satisfying in minimum uncertainty relation. In recently, states have generates with electrons by Bose-Einstein condensations and particles oscillations. Also,this states are satisfying in minimum uncertainty relation, with this difference that parameters in this states are the first and second moments of soin operators instead of position and momentum operators.The similarity phenomenon about squeezing photon is exist for spin with that distance. The source of spin squeezing in multi-qubit states is entanglement. One applecations of spin squeezing is to detect quantum entanglement which plays a key role in both the foundations of quantum physics and quantum computation processing. In recent years, spin squeezing stsate parameters have close relation with entanglement measure, concurrence, that we can characterize entanglement for a class of many-body spin- states. In reality, spin squeezing parameters are witnesse for many bode entanglement. In this paper; we study relation betweenspin squeezed states and entanglement. Then; we stuy the squeezing spin for -mode and -mode entangled coherent states.
In order to witness multipartite correlations beyond pairwise entanglement, we study the spin-squeezing evolution of a spin-1/2 ensemble in environments with quantum phase transitions. Each spin half of the ensemble evolves under its own decoherence channel, which is modeled by a central spin 1/2 surrounded by a spin-1/2 XYXYXY chain. We employ four spin-squeezing parameters to describe squeezing, and their expressions at time ttt are analytically calculated for the spin ensemble in a collective initial state. It is found that spin squeezing of an auxiliary ensemble signals very well the critical regions of the environment. Quantum fluctuations of the environment accelerate the decay of spin squeezing and dramatically change spin squeezing.