One-shot bounds improve quantum entanglement across noisy connections
One-shot entanglement generation and distillation via Petz recovery and binary hypothesis testing
Information Theory
Summary
When two distant labs want to share entanglement through noisy links, it is hard to know how much can truly be shared accurately. The authors connect this problem to deciding between two quantum states, a task called binary hypothesis testing. They propose new mathematical bounds that tightly estimate entanglement generation and distillation capability in one attempt, even with imperfect states. Their approach also shows how to convert entanglement generation methods into entanglement transmission ones with minimal loss.
What this means in practice
- •For quantum communication engineers: Optimize entanglement sharing protocols over noisy quantum channels using explicit one-shot bounds and low-error recovery guarantees.
- •For quantum hardware designers: Design quantum devices with guaranteed entanglement transmission rates and error margins based on realistic one-shot performance analyses.
Authors
Matthew Can, Mark M. Wilde
Abstract
How much entanglement can two distant laboratories share when their connection is noisy? We relate this question to deciding which of two quantum hypotheses is present. Our one-shot bounds apply to entanglement generation over a quantum channel and to one-way entanglement distillation from a shared state. We use Cheng's trace inequality to bound the infidelity of a Petz decoder in terms of a binary hypothesis testing cost. Applying the inequality before averaging over codes reduces the error analysis to computing a second moment of random subspaces. The proof covers every integer target dimension and treats rank-deficient states explicitly. A corollary expresses the achievable entanglement through hypothesis-testing coherent information, with a single logarithmic error slack and exact integer rounding. We also prove an error-preserving conversion from entanglement generation codes to entanglement transmission codes: the target dimension decreases by only a constant factor at fixed error, and the decoder is the original decoder followed by local processing. Consequently, for both entanglement generation and entanglement transmission, arbitrary pure reference-input states yield the same coherent-information rate, second-order Gaussian correction at the original error tolerance, and explicit achievable logarithmic remainder. For commuting testing hypotheses, the logarithmic remainder improves to a constant. These results give a direct route from binary distinguishability to explicit recovery guarantees and finite-resource quantum communication rates.