Relating different quantum generalizations of the conditional Renyi entropy

Abstract

Recently a new quantum generalization of the Renyi divergence and the corresponding conditional Renyi entropies was proposed. Here we report on a surprising relation between conditional Renyi entropies based on this new generalization and conditional Renyi entropies based on the quantum relative Renyi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Renyi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Renyi entropies and derive a new entropic uncertainty relation.

10 pages, 1 figure

References in corpus (4)

• Leftover Hashing Against Quantum Side Information
• Fundamental bound on the reliability of quantum information transmission
• On the strong converses for the quantum channel capacity theorems
• The Converse Part of The Theorem for Quantum Hoeffding Bound

Cited by in corpus (51)

• Entropic Uncertainty Relations and their Applications
• Entropy accumulation
• Correlation Detection and an Operational Interpretation of the Renyi Mutual Information
• Renyi generalizations of the conditional quantum mutual information
• On Variational Expressions for Quantum Relative Entropies
• Strong converse rates for quantum communication
• Operational Interpretation of Renyi Information Measures via Composite Hypothesis Testing Against Product and Markov Distributions
• Entropy of a quantum channel
• A family of generalized quantum entropies: definition and properties
• Coherence and entanglement measures based on Rényi relative entropies
• Investigating Properties of a Family of Quantum Renyi Divergences
• Uniform Random Number Generation from Markov Chains: Non-Asymptotic and Asymptotic Analyses
• Rényi generalizations of quantum information measures
• Non-Asymptotic Classical Data Compression with Quantum Side Information
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification
• Chain rules for quantum Rényi entropies
• Pretty good measures in quantum information theory
• Partially smoothed information measures
• Postselection-free learning of measurement-induced quantum dynamics
• Quantum reverse hypercontractivity
• Leftover hashing from quantum error correction: Unifying the two approaches to the security proof of quantum key distribution
• Secure uniform random number extraction via incoherent strategies
• Duality of channels and codes
• Bipartite separability of one parameter families of states using conditional quantum relative Tsallis entropy
• Quantum realism: axiomatization and quantification
• The strong converse exponent of discriminating infinite-dimensional quantum states
• Conditional entropic uncertainty relations for Tsallis entropies
• Maximum one-shot dissipated work from Renyi divergences
• Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks
• Tight lower bound on the error exponent of classical-quantum channels
• Inevitability of knowing less than nothing
• Decomposition Rules for Quantum Rényi Mutual Information with an Application to Information Exclusion Relations
• Biseparability of noisy pseudopure, W and GHZ states using conditional quantum relative Tsallis entropy
• Geometric monotones of violations of quantum realism
• Quantum Polarization of Qudit Channels
• Entropically secure encryption with faster key expansion
• Generalized Rényi entropy accumulation theorem and generalized quantum probability estimation
• General framework of quantum complementarity from a measurement-based perspective
• High probability decoupling via approximate unitary designs and efficient relative thermalisation
• Adversarial quantum channel discrimination
• One-shot information-theoretical approaches to fluctuation theorems
• One-shot multi-sender decoupling and simultaneous decoding for the quantum MAC
• Asymptotically Secure Network Code for Active Attacks and its Application to Network Quantum Key Distribution
• Random coding exponents galore via decoupling
• Secrecy and Robustness for Active Attack in Secure Network Coding and its Application to Network Quantum Key Distribution
• Comment on "Conditional Decoupling of Quantum Information"
• Equivalence of three classical algorithms with quantum side information: Privacy amplification, error correction, and data compression
• A fixed-point algorithm for matrix projections with applications in quantum information
• Approximate Quantum Error Correction with 1D Log-Depth Circuits
• Finite-size secret-key rates of discrete modulation continuous-variable quantum key distribution under Gaussian attacks
• Rényi divergence inequalities via interpolation, with applications to generalised entropic uncertainty relations