Dense network coding computes group operations over multiaccess networks with half the classical communication cost using shared entanglement plus quantum channels, and yields measurement-device-independent quantum key growing.
Tomamichel.Quantum Information Processing with Finite Resources, volume 5 of SpringerBriefs in Mathematical Physics
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abstract
One of the predominant challenges when engineering future quantum information processors is that large quantum systems are notoriously hard to maintain and control accurately. It is therefore of immediate practical relevance to investigate quantum information processing with limited physical resources, for example to ask: How well can we perform information processing tasks if we only have access to a small quantum device? Can we beat fundamental limits imposed on information processing with classical resources? This book will introduce the reader to the mathematical framework required to answer such questions. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including R\'enyi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of R\'enyi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed.
representative citing papers
No Rényi-type divergence obeying DPI, tensor additivity and matched cq conditioning admits a universal off-diagonal quantum focusing inequality.
1D translation-invariant Gibbs states at positive temperature exhibit superexponential decay of Belavkin-Staszewski conditional mutual information, enabling efficient learning from local measurements and tensor network approximations.
citing papers explorer
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Communication Advantages from Quantum Dense Network Coding
Dense network coding computes group operations over multiaccess networks with half the classical communication cost using shared entanglement plus quantum channels, and yields measurement-device-independent quantum key growing.
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No off-diagonal quantum focusing for R\'enyi divergences
No Rényi-type divergence obeying DPI, tensor additivity and matched cq conditioning admits a universal off-diagonal quantum focusing inequality.
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Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
1D translation-invariant Gibbs states at positive temperature exhibit superexponential decay of Belavkin-Staszewski conditional mutual information, enabling efficient learning from local measurements and tensor network approximations.