PIRSA:25050048 Scientific Series Quantum Information

DOI10.48660/25050048

Series: Quantum Information

(2025). Approximate entropy accumulation. Perimeter Institute. https://pirsa.org/25050048

Approximate entropy accumulation. Perimeter Institute, May. 28, 2025, https://pirsa.org/25050048 

@misc{ pirsa_PIRSA:25050048,
  doi = {10.48660/25050048},
  url = {https://pirsa.org/25050048},
  author = {},
  keywords = {Quantum Information},
  language = {en},
  title = {Approximate entropy accumulation},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {may},
  note = {PIRSA:25050048 see, \url{https://pirsa.org}}
}

Abstract

The entropy accumulation theorem (EAT) allows us to lower
bound the min-entropy of a state that can be generated by a chain of
quantum channels satisfying a Markov chain condition, and can be used to
prove the security of QKD protocols, including device-independent ones.
However, one of its drawbacks is that it only applies to states with a
fairly rigid structure; in particular, the Markov chain condition must
be satisfied exactly. What happens when we relax this assumption by
allowing the required structure to be satisfies only approximately? Does
doing so lead to interesting applications? We answer both questions by
the affirmative: we present two flavours of approximate EAT, and show
that it can be used to prove the security of parallel device-independent
QKD, and to analyze QKD protocols under source correlations. Along the
way, we will introduce the concept of "approximation chain" which
underpins the new results.
 
This is joint work with Ashutosh Marwah; the talk will cover material
from 2412.06723, 2402.12346, and 2308.11736.

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