- Various forms of "immune passports" or "antibody certificates" are being considered in conversations around reopening economies after periods of social distancing. A critique of such programs focuses on the uncertainty around whether seropositivity means immunity from repeat infection. However, an additional important consideration is that the low positive predictive value of serological tests in the setting of low population seroprevalence and imperfect test specificity will lead to many false-positive passport holders. Here, we pose a simple question: how many false-positive passports could be issued while maintaining herd immunity in the workforce? Answering this question leads to a simple mathematical formula for the minimum requirements of serological tests for a passport program, which depend on the population prevalence and the value of the basic reproductive number, R0. Our work replaces speculation in the press with rigorous analysis, and will need to be considered in policy decisions that are based on individual and population serology results.