Privacy Amplification, Private States, and the Uncertainty Principle

Abstract

We show that three principle means of treating privacy amplification in quantum key distribution, private state distillation, classical privacy amplification, and via the uncertainty principle, are equivalent and interchangeable. By adapting the security proof based on the uncertainty principle, we construct a new protocol for private state distillation which we prove is identical to standard classical privacy amplification. Underlying this approach is a new characterization of private states, related to their standard formulation by the uncertainty principle, which gives a more physical understanding of security in quantum key distribution.

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Cited by in corpus (31)

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• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• Conjectured Strong Complementary Information Tradeoff
• Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory
• Quantum-memory-assisted entropic uncertainty relations
• The information-theoretic costs of simulating quantum measurements
• One-Shot Classical Data Compression with Quantum Side Information and the Distillation of Common Randomness or Secret Keys
• Efficient Quantum Polar Coding
• Polar codes for private and quantum communication over arbitrary channels
• Multipartite secret key distillation and bound entanglement
• Duality of privacy amplification against quantum adversaries and data compression with quantum side information
• Sequential decoding of a general classical-quantum channel
• Quantum polar codes for arbitrary channels
• Polar codes for degradable quantum channels
• Improved quantum entropic uncertainty relations
• Leftover hashing from quantum error correction: Unifying the two approaches to the security proof of quantum key distribution
• Efficient Quantum Polar Codes Requiring No Preshared Entanglement
• A transform of complementary aspects with applications to entropic uncertainty relations
• Duality of channels and codes
• The Physics of Quantum Information: Complementarity, Uncertainty, and Entanglement
• Polar codes for private classical communication
• Bounds on Information Combining With Quantum Side Information
• Optimal State Merging Without Decoupling
• W-like bound entangled states and secure key distillation
• Optimal Universal Uncertainty Relations
• Performance of polar codes for quantum and private classical communication
• Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole
• The reduction of entropy uncertainty for qutrit system under non-Markov noisy environment
• The dynamics of entropy uncertainty for qutrit system under the random telegraph noise
• Equivalence of three classical algorithms with quantum side information: Privacy amplification, error correction, and data compression