Asymptotic quantification of entanglement with a single copy
This work addresses the challenge of measuring entanglement in quantum technologies, providing a novel theoretical framework for benchmarking distillation performance, though it is incremental in refining existing axiomatic methods.
The paper tackled the problem of quantifying entanglement for quantum information tasks by introducing a new benchmarking approach focused on error rates rather than yield, and showed that entanglement testing and distillation metrics coincide under non-entangling operations, with the asymptotic figure of merit being the reverse relative entropy of entanglement, a single-letter quantity computable from a single copy.
Despite the central importance of quantum entanglement in quantum technologies, the understanding of the optimal ways to exploit it is still beyond our reach, and even measuring entanglement in an operationally meaningful way is prohibitively difficult. Here we study two fundamental tasks in the processing of entanglement: entanglement testing, which is a quantum state discrimination problem concerned with entanglement detection in the many-copy regime, and entanglement distillation, concerned with purifying entanglement from noisy entangled states. We introduce a way of benchmarking the performance of distillation that focuses on the best achievable error rather than its yield in the asymptotic limit. When the underlying set of operations used for entanglement distillation is the axiomatic class of non-entangling operations, we show that the two figures of merit for entanglement testing and distillation coincide. We solve both problems by proving a generalised quantum Sanov's theorem, enabling the exact evaluation of asymptotic error rates of composite quantum hypothesis testing. We show in particular that the asymptotic figure of merit is given by the reverse relative entropy of entanglement, a single-letter quantity that can be evaluated using only a single copy of a quantum state -- a distinct feature among measures of entanglement that quantify the optimal performance of information-theoretic tasks.