Semi-definite optimization of the measured relative entropies of quantum states and channels

arXiv:2406.19060 · quant-ph, cs.IT, math-ph, math.IT, math.MP, math.OC · Submitted 2024-06-27 · Read on arXiv

quant-ph, cs.IT, math-ph, math.IT, math.MP, math.OC

Submitted: 2024-06-27

Updated: 2025-10-18

Comments: v3: 39 pages, expanded Propositions 7 and 13

Journal ref: Proceedings of the Royal Society A, vol. 482, no. 2346, pages 20251063, Sept. 2026

DOI: 10.1098/rspa.2025.1063

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Transformer — 8× in this paper · explained in 2 episodes
• Objective Function — 7× in this paper · explained in 2 episodes
• Entanglement — 5× in this paper · explained in 3 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Generalization — 4× in this paper · explained in 13 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Additivity — 1× in this paper · explained in 1 episode
• Fidelity — 1× in this paper · explained in 2 episodes
• Hybrid Approach — 1× in this paper · explained in 4 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes

Sources

• Asymptotic Error Rates in Quantum Hypothesis Testing
• On Variational Expressions for Quantum Relative Entropies
• Infinite Dimensional Asymmetric Quantum Channel Discrimination
• Quantum computer-enabled receivers for optical communication
• An invitation to the sample complexity of quantum hypothesis testing
• Memory effects in quantum channel discrimination
• The Perfect Distinguishability of Quantum Operations
• Rational approximations of operator monotone and operator convex functions
• Lieb's concavity theorem, matrix geometric means, and semidefinite optimization
• Optimal self-concordant barriers for quantum relative entropies
• Distinguishability and Accessible Information in Quantum Theory
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Adaptive versus non-adaptive strategies for quantum channel discrimination
• Optimising the relative entropy under semidefinite constraints
• Principles of Quantum Communication Theory: A Modern Approach
• Some continuity properties of quantum R'enyi divergences
• The Converse Part of The Theorem for Quantum Hoeffding Bound
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Locally-Measured R'enyi Divergences
• Energy-constrained diamond norms and their use in quantum information theory

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