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A search for CP violation with an entangled system of Ξ-Ξ¯+ pairs is performed, using (10,087±44)×106 J/ψ events collected with the BESIII experiment. A nine-dimensional helicity amplitude is used to fit e+e-→J/ψ→Ξ-Ξ¯+ and its subsequent decays. The Ξ- and Ξ¯+ decay parameters are determined with higher precision compared to the best results reported so far. Furthermore, the strong phase difference, (δP-δS)=(0.3±1.2±0.2)×10-2 rad, and the weak phase difference, (ζP-ζS)=(-0.2±1.2±0.1)×10-2 rad, are directly determined. These are the most precise measurements to date. The CP asymmetry observables ACPΞ=(-7.8±4.8±0.8)×10-3 and ΔφCPΞ=(0.6±5.1±0.2)×10-3 rad are determined, which are consistent with CP conservation. In addition, independent measurements of the Λ decay parameter and CP asymmetry ACPΛ=(-2.9±4.3±0.7)×10-3 are also obtained, which are in agreement with the previous measurements, but with much improved precision.