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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Generalised Entropy Accumulation.

Tony Metger1, Omar Fawzi2, David Sutter3

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This study introduces a generalized entropy accumulation theorem (EAT) for sequential processes with updated side information. It provides a lower bound on output min-entropy, enhancing security proofs for cryptographic protocols like randomness expansion and quantum key distribution.

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Area of Science:

  • Quantum Information Theory
  • Cryptography
  • Mathematical Physics

Background:

  • The standard Entropy Accumulation Theorem (EAT) has limitations due to its restrictive model of side information.
  • Existing cryptographic protocols often involve complex sequential processes with evolving side information.

Purpose of the Study:

  • To generalize the EAT for sequential processes with updatable side information.
  • To establish a lower bound for the min-entropy of outputs conditioned on final side information.
  • To broaden the applicability of EAT in cryptographic security proofs.

Main Methods:

  • Development of a generalized non-signalling condition for sequential processes.
  • Application of a new variant of Uhlmann's theorem.
  • Derivation of new chain rules for Rényi divergence and entropy.

Main Results:

  • A generalized EAT is proven, bounding the min-entropy of outputs based on individual step von Neumann entropies.
  • The generalized EAT accommodates more flexible models of side information compared to the original EAT.
  • The theorem is applied to provide the first multi-round security proof for blind randomness expansion and simplify the E91 QKD protocol analysis.

Conclusions:

  • The generalized EAT offers a more versatile tool for analyzing quantum cryptographic protocols.
  • The new mathematical tools developed may have independent theoretical significance.
  • This work facilitates more accessible and broader security proofs in quantum cryptography.