In this paper, we consider the multi-user detection problem in a multiple-input multiple-output (MIMO) system, where the number of receive antennas at the base station (BS) grows infinitely large. We propose a new performance metric, called antenna efficiency, to characterize how fast the vector error probability (VEP) decreases as the number of receive antennas increases in the large system limit. We analyze the optimal maximum-likelihood (ML) detector and the simple zero-forcing (ZF) detector and prove that their antenna efficiency admits a simple closed form, which quantifies the impacts of the user-to-antenna ratio, the signal-to-noise ratio (SNR), and the constellation set on the VEP. Numerical results show that our analysis can well describe the empirical detection error performance in a realistic massive MIMO system.