We present an HST/ACS weak gravitational lensing analysis of 13 massive high-redshift (z_median=0.88) galaxy clusters discovered in the South Pole Telescope (SPT) Sunyaev-Zeldovich Survey. This study is part of a larger campaign that aims to robustly calibrate mass-observable scaling relations over a wide range in redshift to enable improved cosmological constraints from the SPT cluster sample. We introduce new strategies to ensure that systematics in the lensing analysis do not degrade constraints on cluster scaling relations significantly. First, we efficiently remove cluster members from the source sample by selecting very blue galaxies in V-I colour. Our estimate of the source redshift distribution is based on CANDELS data, where we carefully mimic the source selection criteria of the cluster fields. We apply a statistical correction for systematic photometric redshift errors as derived from Hubble Ultra Deep Field data and verified through spatial cross-correlations. We account for the impact of lensing magnification on the source redshift distribution, finding that this is particularly relevant for shallower surveys. Finally, we account for biases in the mass modelling caused by miscentring and uncertainties in the concentration-mass relation using simulations. In combination with temperature estimates from Chandra we constrain the normalisation of the mass-temperature scaling relation ln(E(z) M_500c/10^14 M_sun)=A+1.5 ln(kT/7.2keV) to A=1.81^{+0.24}_{-0.14}(stat.) +/- 0.09(sys.), consistent with self-similar redshift evolution when compared to lower redshift samples. Additionally, the lensing data constrain the average concentration of the clusters to c_200c=5.6^{+3.7}_{-1.8}.
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