Generalised entropy accumulation

Abstract

Consider a sequential process in which each step outputs a system $A_i$ and updates a side information register $E$. We prove that if this process satisfies a natural "non-signalling" condition between past outputs and future side information, the min-entropy of the outputs $A_1,\dots ,A_n$ conditioned on the side information $E$ at the end of the process can be bounded from below by a sum of von Neumann entropies associated with the individual steps. This is a generalisation of the entropy accumulation theorem (EAT), which deals with a more restrictive model of side information: there, past side information cannot be updated in subsequent rounds, and newly generated side information has to satisfy a Markov condition. Due to its more general model of side-information, our generalised EAT can be applied more easily and to a broader range of cryptographic protocols. As examples, we give the first multi-round security proof for blind randomness expansion and a simplified analysis of the E91 QKD protocol. The proof of our generalised EAT relies on a new variant of Uhlmann's theorem and new chain rules for the Renyi divergence and entropy, which might be of independent interest.

42 pages; v2 expands introduction but does not change any results; in FOCS 2022

References in corpus (4)

• Post-selection technique for quantum channels with applications to quantum cryptography
• Private Randomness Expansion With Untrusted Devices
• Security of quantum key distribution from generalised entropy accumulation
• Generalised entropy accumulation

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• Quantum key distribution rates from non-symmetric conic optimization
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• Device-independent certification of desirable properties with a confidence interval
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• The role of entanglement in energy-restricted communication and randomness generation
• Quantum Random Number Generation with Partial Source Assumptions
• Long-distance device-independent quantum key distribution with standard optics tools
• Uhlmann's theorem for measured divergences
• One-Shot Distributed Source Simulation: As Quantum as it Can Get
• Asymptotic Equipartition Theorems in von Neumann algebras
• Finite-size security of QKD: comparison of three proof techniques
• Device-independent secure correlations in sequential quantum scenarios