Efficient optimization of the quantum relative entropy

DOI10.1088/1751-8121/aab285zbMath1388.81080arXiv1705.06671OpenAlexW2791458179WikidataQ62556708 ScholiaQ62556708MaRDI QIDQ4639620

Hamza Fawzi, Omar Fawzi

Publication date: 9 May 2018

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.06671

zbMATH Keywords

convex optimizationvon Neumann entropyquantum relative entropyentanglement measuresquantum capacityquantum conditional mutual information

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Channel models (including quantum) in information and communication theory (94A40) Quantum coherence, entanglement, quantum correlations (81P40) Coding theorems (Shannon theory) (94A24) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (12)

Shannon’s information theory 70 years on: applications in classical and quantum physics ⋮ Long-step path-following algorithm for quantum information theory: some numerical aspects and applications ⋮ Optimal Self-Concordant Barriers for Quantum Relative Entropies ⋮ Performance enhancements for a generic conic interior point algorithm ⋮ Entanglement monogamy via multivariate trace inequalities ⋮ Quantum conditional relative entropy and quasi-factorization of the relative entropy ⋮ Squashed entanglement, \(\mathbf {k}\)-extendibility, quantum Markov chains, and recovery maps ⋮ Semidefinite approximations of the matrix logarithm ⋮ Primal-Dual Interior-Point Methods for Domain-Driven Formulations ⋮ Geometric Rényi divergence and its applications in quantum channel capacities ⋮ On composite quantum hypothesis testing ⋮ Recovery map stability for the data processing inequality

Uses Software

• Matlab
• Quantinf

Cites Work

• Lieb's concavity theorem, matrix geometric means, and semidefinite optimization
• Quantum conditional mutual information and approximate Markov chains
• Relative entropy optimization and its applications
• Squashed entanglement, \(\mathbf {k}\)-extendibility, quantum Markov chains, and recovery maps
• The capacity of a quantum channel for simultaneous transmission of classical and quantum information
• On the semidefinite representation of real functions applied to symmetric matrices
• Efficient Approximation of Quantum Channel Capacities
• Classical deterministic complexity of Edmonds' Problem and quantum entanglement
• SUFFICIENCY OF CHANNELS OVER VON NEUMANN ALGEBRAS
• Quantifying Entanglement
• Approximate Degradable Quantum Channels
• Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem

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