Entropy Accumulation under Post-Quantum Cryptographic Assumptions
- URL: http://arxiv.org/abs/2307.00559v1
- Date: Sun, 2 Jul 2023 12:52:54 GMT
- Title: Entropy Accumulation under Post-Quantum Cryptographic Assumptions
- Authors: Ilya Merkulov, Rotem Arnon-Friedman
- Abstract summary: In device-independent (DI) quantum protocols, the security statements are oblivious to the characterization of the quantum apparatus.
We present a flexible framework for proving the security of such protocols by utilizing a combination of tools from quantum information theory.
- Score: 4.416484585765028
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In device-independent (DI) quantum protocols, the security statements are
oblivious to the characterization of the quantum apparatus - they are based
solely on the classical interaction with the quantum devices as well as some
well-defined assumptions. The most commonly known setup is the so-called
non-local one, in which two devices that cannot communicate between themselves
present a violation of a Bell inequality. In recent years, a new variant of DI
protocols, that requires only a single device, arose. In this novel research
avenue, the no-communication assumption is replaced with a computational
assumption, namely, that the device cannot solve certain post-quantum
cryptographic tasks. The protocols for, e.g., randomness certification, in this
setting that have been analyzed in the literature used ad hoc proof techniques
and the strength of the achieved results is hard to judge and compare due to
their complexity. Here, we build on ideas coming from the study of non-local DI
protocols and develop a modular proof technique for the single-device
computational setting. We present a flexible framework for proving the security
of such protocols by utilizing a combination of tools from quantum information
theory, such as the entropic uncertainty relation and the entropy accumulation
theorem. This leads to an insightful and simple proof of security, as well as
to explicit quantitative bounds. Our work acts as the basis for the analysis of
future protocols for DI randomness generation, expansion, amplification and key
distribution based on post-quantum cryptographic assumptions.
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