Tight any-shot quantum decoupling

2026-02-19

AI Summary

This work investigates the error characterization and performance limits of quantum information decoupling in arbitrary-shot settings, with a particular focus on decoupling error exponents under low resource rates. By introducing the quantum relative entropy distance, the authors establish for the first time a tight one-shot decoupling theorem, providing a sharp upper bound on the decoupling error expressed via the sandwiched Rényi conditional entropy. This framework is extended to the asymptotic i.i.d. regime and yields single-letter error exponents for quantum state merging, as well as achievable error exponents for entanglement distillation and quantum channel coding. Tightness of these bounds is demonstrated in the high-rate regime for maximally correlated states and generalized dephasing channels, offering precise performance benchmarks for related quantum protocols.

Technology Category

• Machine Learning: Information Theory
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling theorem formulated in terms of quantum relative entropy distance, with the decoupling error bounded by two sandwiched Rényi conditional entropies. In the asymptotic i.i.d. setting of standard information decoupling via partial trace, we show that this bound is ensemble-tight in quantum relative entropy distance and thereby yields a characterization of the associated decoupling error exponent in the low-cost-rate regime. Leveraging this framework, we derive several operational applications formulated in terms of purified distance: (i) a single-letter expression for the exact error exponent of quantum state merging in terms of Petz-Rényi conditional entropies, and (ii) regularized expressions for the achievable error exponent of entanglement distillation and quantum channel coding in terms of Petz-Rényi coherent informations. We further prove that these achievable bounds are tight for maximally correlated states and generalized dephasing channels, respectively, for the high distillation-rate/coding-rate regimes.

Problem

• quantum decoupling
• one-shot
• error exponent
• quantum information theory
• Rényi entropy

Innovation

• one-shot decoupling
• quantum relative entropy
• Rényi conditional entropy
• error exponent
• quantum state merging