Generalised entropy accumulation
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Date
2022
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Conference Paper
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Abstract
The min-entropy of a quantum system A conditioned on another quantum system E describes how much randomness can be extracted from A with respect to an adversary in possession of E. This quantity plays a crucial role in quantum cryptography: the security proofs of many quantum cryptographic protocols reduce to showing a lower bound on such a min-entropy. Here, we develop a new tool, called generalised entropy accumulation, for computing such bounds. Concretely, we 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),..., 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) [1], 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. In particular, it is the first general tool that is applicable to mistrustful device-independent cryptography. To demonstrate this, we give the first security proof for blind randomness expansion [2] against general adversaries. Furthermore, our generalised EAT can be used to give improved security proofs for quantum key distribution [3], and also has applications beyond quantum cryptography.
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published
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2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)
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Pages / Article No.
844 - 850
Publisher
IEEE
Event
63rd IEEE Symposium on Foundations of Computer Science (FOCS 2022)
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Subject
entropy; min-entropy; quantum cryptography; device-independence
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Funding
185902 - QSIT - Quantum Science and Technology (SNF)
188541 - Information-theoretic limits to time measurements (SNF)
188541 - Information-theoretic limits to time measurements (SNF)