The properties of the ferimonic entangled states resulting from the projective measurements in the Gauss–Bonnet spacetime are studied. It is found that the degree of entanglement, for projection onto double particles state, increases monotonously as the Hawking temperature T increases but decreases monotonously as the frequency of the detected particles increases; and for projection onto single particle state, the particle states are entangled for spin picture but are separable states for occupation number picture as \(T\rightarrow 0\), while the particle states for the both pictures are entangled as \(T\rightarrow \infty \). It is also shown that the Gauss–Bonnet coefficient \(\alpha \) and dimension d of the spacetime will affect the entanglement greatly.

研究了在高斯-邦尼特时空中的投射测量所产生的费米子纠缠态的性质。可以发现，投影到双粒子状态的纠缠度随霍金温度T的升高而单调增加，但随着被检测粒子的频率增加而单调降低。对于投影到单个粒子状态，对于自旋图片，粒子状态是纠缠的，但是对于占用编号图片，它们的可分状态是\（T \ rightarrow 0 \），而对于两个图片的粒子状态，它们的纠缠态都是\（T \ rightarrow \ infty \）。还显示了高斯-帽子系数\（\ alpha \）和维数d 时空的变化将极大地影响纠缠。