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In the context of topcolor-assisted techicolor($TC2$) models, we investigatethe feasibility of detecting the non-universal gauge boson $Z^{'}$ in thefuture high-energy linear $e^{+}e^{-}$ collider($LC$) experiments by performing$\chi^{2}$ analysis via studying its virtual effects on the processes$e^{+}e^{-}\to f\bar{f}$ with $f=\tau$, $\mu$, b, and c. We find that thenon-universal gauge boson $Z^{'}$ is most sensitive to the process$e^{+}e^{-}\to \tau\bar{\tau}$. Discovery limits of the $Z^{'}$ mass$M_{Z^{'}}$ can be enhanced by the suitably polarized beams. If we assume thatpolarization of electron beam and positron beam are 80% and 60%, the $LC$experiment with $\sqrt{s}=500GeV$ and $\pounds_{int}=340fb^{-1}$ can explore$M_{Z^{'}}$ up to 8$TeV$ for the coupling parameter $K_{1}\leq$0.8 at 95% $CL$.Comment: 11 pages, 2 figure

Preparation of the W State of Atoms in a Single Cavity or N Distant Cavities by Photon Interference