ETD

• conic programming
• distillable entanglement
• entanglement measures
• entanglement theory
• quantum hypothesis testing
• quantum information theory
• quantum resource theories

Quantum entanglement is a unique feature of quantum mechanics and a key resource for quantum information processing. In realistic scenarios, entanglement is usually available only in noisy mixed states. For this reason, entanglement distillation is required to convert many imperfect copies into a smaller number of maximally entangled states using local operations and classical communication. In the asymptotic regime, the distillation rate provides a quantitative measure of the entanglement content of a quantum state. Entanglement distillation can be analyzed from two complementary perspectives: as an entanglement measure and as a problem in quantum hypothesis testing, in particular entanglement testing. Because local operations and classical communication are difficult to characterize, we consider larger and more tractable classes of operations, such as those preserving positivity under partial transposition. Within the quantum hypothesis testing framework, we introduce the distillable entanglement error exponent, which describes the asymptotic decay of error probabilities. For isotropic states, we show that this exponent coincides for different classes of admissible operations. From the perspective of entanglement measures, we also introduce a new measure that provides a tighter upper bound on the distillable entanglement. These results contribute to a deeper understanding of entanglement as a quantum resource.