We report the strictest observational verification of CPT invariance in the
photon sector, as a result of gamma-ray polarization measurement of distant
gamma-ray bursts (GRBs), which are brightest stellar-size explosions in the
universe. We detected the gamma-ray polarization of three GRBs with high
significance, and the source distances may be constrained by a well-known
luminosity indicator for GRBs. For the Lorentz- and CPT-violating dispersion
relation E_{\pm}^2=p^2 \pm 2\xi p^3/M_{Pl}, where \pm denotes different
circular polarization states of the photon, the parameter \xi is constrained as
|\xi|<O(10^{-15}). Barring precise cancellation between quantum gravity effects
and dark energy effects, the stringent limit on the CPT-violating effect leads
to the expectation that quantum gravity presumably respects the CPT invariance.Comment: 4 pages; accepted for publication in Physical Review Letters;
redshift estimates of GRBs changed (i.e z=0.382 was wrong for GRB 110721A)
and calculations of \xi limit improved from the previous versio