Asymptotic quantification of entanglement with a single copy

A new theoretical result solves two fundamental quantum information tasks—entanglement testing and entanglement distillation—by proving a generalized quantum Sanov's theorem. The key finding is that the asymptotic error exponent for both tasks equals the reverse relative entropy of entanglement, a quantity that can be computed from a single copy of a quantum state without regularization. This sidesteps the long-standing problem of regularized formulas that require evaluating limits over many copies of a state, providing the first single-letter asymptotic solution valid for all quantum states in entanglement manipulation under non-entangling operations.