The Smooth Entropy Formalism for von Neumann Algebras

Abstract

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

v3: 28 pages, published version

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Cited by in corpus (31)

• Advances in Quantum Cryptography
• Distributing Secret Keys with Quantum Continuous Variables: Principle, Security and Implementations
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• Exponential Decay of Correlations Implies Area Law
• Continuous-variable measurement-device-independent quantum key distribution: Composable security against coherent attacks
• Reverse Reconciliation Continuous Variable Quantum Key Distribution Based on the Uncertainty Principle
• Position-Momentum Uncertainty Relations in the Presence of Quantum Memory
• Decoupling with unitary approximate two-designs
• Finite-Size Security for Discrete-Modulated Continuous-Variable Quantum Key Distribution Protocols
• Rényi divergences as weighted non-commutative vector valued $L_p$-spaces
• Certified Quantum Random Numbers from Untrusted Light
• Framework for resource quantification in infinite-dimensional general probabilistic theories
• Quantum Bilinear Optimization
• Continuous-Variable Protocol for Oblivious Transfer in the Noisy-Storage Model
• Security of discrete-modulated continuous-variable quantum key distribution
• Capacity estimation and verification of quantum channels with arbitrarily correlated errors
• One-shot holography
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
• Improved finite-size key rates for discrete-modulated continuous variable quantum key distribution under coherent attacks
• Relative entropy of coherent states on general CCR algebras
• Quantum Brascamp-Lieb Dualities
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Refined finite-size analysis of binary-modulation continuous-variable quantum key distribution
• State convertibility in the von Neumann algebra framework
• Certified Randomness from a Two-Level System in a Relativistic Quantum Field
• Fidelity of density operator in an operator-algebraic framework
• Quantum teleportation in the commuting operator framework
• Detecting Quantum Capacities of Continuous-Variable Quantum Channels
• Asymptotic Equipartition Theorems in von Neumann algebras