We present a new method to measure the redshift-dependent galaxy bias by combining information from the galaxy density field and the weak lensing field. This method is based on Amara et al. (2012), where they use the galaxy density field to construct a bias-weighted convergence field kg. The main difference between Amara et al. (2012) and our new implementation is that here we present another way to measure galaxy bias using tomography instead of bias parameterizations. The correlation between kg and the true lensing field k allows us to measure galaxy bias using different zero-lag correlations, such as <kgk>/<kk> or <kgkg>/<kgk>. Our method measures the linear bias factor on linear scales under the assumption of no stochasticity between galaxies and matter. We use the MICE simulation to measure the linear galaxy bias for a flux-limited sample (i < 22.5) in tomographic redshift bins using this method. This paper is the first that studies the accuracy and systematic uncertainties associated with the implementation of the method, and the regime where it is consistent with the linear galaxy bias defined by projected 2-point correlation functions (2PCF). We find that our method is consistent with linear bias at the percent level for scales larger than 30 arcmin, while nonlinearities appear at smaller scales. This measurement is a good complement to other measurements of bias, since it does not depend strongly on sigma8 as the 2PCF measurements. We apply this method to the Dark Energy Survey Science Verification data in a follow-up paper.
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