One-Shot Classical Data Compression with Quantum Side Information and the Distillation of Common Randomness or Secret Keys

Abstract

The task of compressing classical information in the one-shot scenario is studied in the setting where the decompressor additionally has access to some given quantum side information. In this hybrid classical-quantum version of the famous Slepian-Wolf problem, the smooth max-entropy is found to govern the number of bits into which classical information can be compressed so that it can be reliably recovered from the compressed version and quantum side information. Combining this result with known results on privacy amplification then yields bounds on the amount of common randomness and secret key that can be recovered in one-shot from hybrid classical-quantum systems using one-way classical communication.

7 pages, comments welcome. v2: minor errors fixed. v3 final version for publication

References in corpus (10)

• Distillation of secret key and entanglement from quantum states
• The Quantum Chernoff Bound
• Coding Theorem and Strong Converse for Quantum Channels
• Leftover Hashing Against Quantum Side Information
• Noisy channel coding via privacy amplification and information reconciliation
• Smooth Renyi Entropies and the Quantum Information Spectrum
• Distilling entanglement from arbitrary resources
• Generalized relative entropies and the capacity of classical-quantum channels
• Physical Underpinnings of Privacy
• Duality of privacy amplification against quantum adversaries and data compression with quantum side information

Cited by in corpus (46)

• Security in Quantum Cryptography
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
• Max- relative entropy of coherence: an operational coherence measure
• Noisy channel coding via privacy amplification and information reconciliation
• Beyond heat baths: Generalized resource theories for small-scale thermodynamics
• The information-theoretic costs of simulating quantum measurements
• The Link between Entropic Uncertainty and Nonlocality
• Identifying the Information Gain of a Quantum Measurement
• Quantum Achievability Proof via Collision Relative Entropy
• Improved DIQKD protocols with finite-size analysis
• The Smooth Entropy Formalism for von Neumann Algebras
• Duality of privacy amplification against quantum adversaries and data compression with quantum side information
• Strong converse theorems using Rényi entropies
• State-Dependent Approach to Entropic Measurement-Disturbance Relations
• Smooth Entropy Bounds on One-Shot Quantum State Redistribution
• Relative Thermalization
• Security bounds for efficient decoy-state quantum key distribution
• Non-Asymptotic Classical Data Compression with Quantum Side Information
• Sequential decoding of a general classical-quantum channel
• Simple security proof of coherent-one-way quantum key distribution
• Pretty good measures in quantum information theory
• Maximum and minimum entropy states yielding local continuity bounds
• Convex-split and hypothesis testing approach to one-shot quantum measurement compression and randomness extraction
• Finite-Key Analysis for Coherent One-Way Quantum Key Distribution
• One-sided Measurement-Device-Independent Quantum Key Distribution
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
• Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation
• Device-independent quantum key distribution over 100 km with single atoms
• The Physics of Quantum Information: Complementarity, Uncertainty, and Entanglement
• Security of differential phase shift QKD from relativistic principles
• Quantum key distribution with finite resources: Taking advantage of quantum noise
• The future of secure communications: device independence in quantum key distribution
• Device independent security of quantum key distribution from monogamy-of-entanglement games
• Enhanced security for multi-detector Quantum Random Number Generators
• One-Shot Hybrid State Redistribution
• One-shot quantum state exchange
• Cone-Restricted Information Theory
• Loss tolerant device-independent quantum key distribution: a proof of principle
• State transfer with quantum side information
• High-Fidelity Coherent-One-Way QKD Simulation Framework for 6G Networks: Bridging Theory and Reality
• Extendibility limits quantum-secured communication and key distillation
• Upper bounds on the leakage of private data and operational approach to markovianity
• Tight relations and equivalences between smooth relative entropies
• Intersection and union of subspaces with applications to communication over authenticated classical-quantum channels and composite hypothesis testing
• Equivalence of three classical algorithms with quantum side information: Privacy amplification, error correction, and data compression