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International Journal of Theoretical Physics

Spin Squeezing in 4-Qubit State Superposed by GHZ State, W State and Symmetric State

Desheng Liu, Song-Song Li

Published Aug 23, 2012• 2 citations
Publisher
DOI
10.1007/s10773-012-1299-z

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The entangled property of Yurke-like state was investigated via spin squeezing.Since the Yurke-like state is superposed by a symmetric state and two special multi-particle states,the entangled property can be studied by investigating superposition coefficient and relative phase's influence on spin squeezing parameter.The analytical results for the optimal squeezed direction and optimal squeezing were obtained via extremum method.It's shown that the spin squeezing parameter monotonously changes with superposition coefficients and periodically changes with relative phase.It is also shown that the more the number of the particles is,the stronger the degree of squeezing will be.
We construct an entanglement witness for many-qubit systems, based on symmetric two-body correlations with two measurement settings. This witness is able to detect the entanglement of some Dicke states for any number of particles and such detection exhibits some robustness against white noise and thermal noise under the Lipkin-Meshkov-Glick Hamiltonian. In addition, it detects the entanglement of spin-squeezed states, with a detection strength that approaches the maximal value for sufficiently large numbers of particles. As spin-squeezed states can be experimentally generated, the properties of the witness with respect to these states may be amenable to experimental investigation. We show that while the witness is unable to detect Greenberger-Horne-Zeilinger (GHZ) states, it is instead able to detect superpositions of Dicke states with GHZ states.