  We introduce eRHL, a program logic for reasoning about relational expectation
properties of pairs of probabilistic programs. eRHL is quantitative, i.e., its
pre- and post-conditions take values in the extended non-negative reals. Thanks
to its quantitative assertions, eRHL overcomes randomness alignment
restrictions from prior logics, including PRHL, a popular relational program
logic used to reason about security of cryptographic constructions, and apRHL,
a variant of PRHL for differential privacy. As a result, eRHL is the first
relational probabilistic program logic to be supported by non-trivial soundness
and completeness results for all almost surely terminating programs. We show
that eRHL is sound and complete with respect to program equivalence,
statistical distance, and differential privacy. We also show that every PRHL
judgment is valid iff it is provable in eRHL. We showcase the practical
benefits of eRHL with examples that are beyond reach of PRHL and apRHL.
