Mathematical proof note · Version 1.0 · October 8, 2026
Global Optimizers of the Binary Masked Mixed-Qubit Bound
National Mobile Communications Research Laboratory and the Frontiers Science Center for Mobile Information Communication and Security, Southeast University, Nanjing 211189, China
Abstract
We determine all global optimizers of the binary masked mixed-qubit coding bound. There is one transition at relative distance 0.20022512064126755…. Below it the unique optimizer is strictly masked; above it the unique optimizer is the optimized unmasked mixed-qubit channel. Exactly two separated optimizers coexist at the transition, and the optimized bound has unequal one-sided derivatives. The proof exhausts the feasible boundary, reduces every interior stationary point to a distance-independent scalar equation, and relates its distance Jacobian to the fixed-distance Hessian determinant. Analytic endpoint estimates and reproducible interval covers establish the complete stationary geometry and the unique value exchange. The accompanying arithmetic verifies functions and derivatives over entire intervals and recomputes every sign from outward enclosures.
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Keywords
binary codes; coding rate bounds; masked mixed-qubit channel; global optimization; interval arithmetic.
中文关键词：二元码；码率上界；混合量子比特信道；全局优化；区间算术。
Suggested citation
S. Yang, "Global Optimizers of the Binary Masked Mixed-Qubit Bound," mathematical proof note, version 1.0, Oct. 8, 2026. [Online]. Available: https://github.com/stalin1943/Coding-Theory-Proof-Notes/blob/main/binary-masked-mixed-qubit-bound/proof.pdf