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In all-optical gate switches that employ the cascade of second-harmonic generation and difference frequency mixing in quasi-phase-matched (QPM) lithium niobate (LN) devices, walkoff between the fundamental and second-harmonic pulses causes crosstalk of the switch. We numerically calculate the switching performance of QPM-LN waveguide devices with consideration for the crosstalk effect, and discuss the favorable choice of the nonlinear optical tensor element for the LN crystal. In the analyses, the device length is maximized for a given bit rate under the condition that the crosstalk is maintained below a critical level that is determined by the allowable power penalty for the switched signal. It is shown that the time offset between the gate and signal pulses can compensate for the walkoff, and can significantly improve the switching efficiency. In ultrafast operation beyond 1 Tbps, the use of the nonlinear optical tensor element d31 is found to be favorable when compared to the use of the commonly used maximum tensor element d33.