We report the spin Knight shift (K_s) and the nuclear spin-lattice relaxation rate (1/T_1) in the vortex state as a function of magnetic field (H) up to 28 T in the high-T_c superconductor TlSr_{2}CaCu_2O_{6.8} (T_c=68 K). At low temperatures well below T_{c}, both K_s and 1/T_1 measured around the middle point between two nearest vortices (saddle point) increase substantially with increasing field, which indicate that the quasiparticle states with an ungapped spectrum are extended outside the vortex cores in a d-wave superconductor. The density of states (DOS) around the saddle point is found to be kappa N_0sqrt{H/H_{c2}}, with kappa=0.5sim0.7 and N_0 being the normal-state DOS.
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