Finite-size quantum key distribution rates from R'enyi entropies using conic optimization

arXiv:2511.10584 · quant-ph · Submitted 2025-11-13 · Read on arXiv

quant-ph

Submitted: 2025-11-13

Updated: 2026-10-14

Comments: 40 pages, 5 figures. v2: Added section 3.4 and extended Remark 1. v3: Added benchmarks. v4: Closer to the published version

Journal ref: PRX Quantum 7, 033051 (2026)

DOI: 10.1103/bf9s-m4jb

Code: https://github.com/araujoms/ConicQKD.jl

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

Terminology

• Trace — 24× in this paper · explained in 2 episodes
• Entanglement — 7× in this paper · explained in 4 episodes
• Distillation — 6× in this paper · explained in 2 episodes
• Benchmark — 5× in this paper · explained in 2 episodes
• Trace Distance — 4× in this paper · explained in 3 episodes
• Core — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Objective Function — 2× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 4 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Security of Quantum Key Distribution
• Security in Quantum Cryptography
• Security of discrete-modulated continuous-variable quantum key distribution
• R'enyi security framework against coherent attacks applied to decoy-state QKD
• Entropy accumulation
• Entropy accumulation with improved second-order term
• Marginal-constrained entropy accumulation theorem
• Security of quantum key distribution from generalised entropy accumulation
• Reliable numerical key rates for quantum key distribution
• The many faces of degeneracy in conic optimization
• Operator convexity along lines, self-concordance, and sandwiched R'enyi entropies
• Quantum key distribution rates from non-symmetric conic optimization
• Privacy amplification and decoupling without smoothing
• Security of quantum key distribution using d-level systems
• Security Proof for Quantum Key Distribution Using Qudit Systems
• Improved finite-size key rates for discrete-modulated continuous variable quantum key distribution under coherent attacks
• Julia: A Fresh Approach to Numerical Computing
• Solving natural conic formulations with Hypatia.jl
• On "A Homogeneous Interior-Point Algorithm for Non-Symmetric Convex Conic Optimization"
• JuMP 1.0: Recent improvements to a modeling language for mathematical optimization

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