Fig. 2: Two ways of benchmarking entanglement distillation.

a,b, Entanglement distillation is the process of converting copies of a noisy entangled quantum state ρ_AB into fewer copies of the pure maximally entangled state Φ₊. To account for physical imperfections in manipulating quantum states, the process is not required to be exact: the resulting states must approximate copies of Φ₊ only to some desired degree of precision, as quantified by the distillation error ε. a, Conventional approaches to distillation focus on maximizing the distillation yield, that is, the number of copies of Φ₊ obtained for each copy of ρ_AB. The error of the procedure is irrelevant as long as it converges to zero in the asymptotic limit as the available number of copies of ρ_AB grows to infinity. For a fixed number of copies, the errors may be large. b, In this paper, we instead focus on minimizing the above error, potentially sacrificing some yield to obtain a higher quality entanglement. Specifically, we require that the distillation error vanishes exponentially fast as the number of available copies of ρ_AB grows, while the total number of maximally entangled states Φ₊ produced in the process is still as large as desired. Accordingly, our figure of merit is not the number of copies produced but the optimal error exponent, that is, the rate of decay of the distillation error, which directly quantifies the quality of the entanglement at the output of the protocol.