On Shor's conjecture on the accessible information of quantum dichotomies

arXiv:2512.11233 · quant-ph · Submitted 2025-12-12 · Read on arXiv

quant-ph

Submitted: 2025-12-12

Updated: 2025-12-12

Comments: 10 pages, 1 figure

Journal ref: IEEE Transactions on Information Theory (Volume: 72, Issue: 10, October 2026)

DOI: 10.1109/TIT.2026.3715995

Code: https://github.com/AlphaAn/somim

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

Terminology

• Generalization — 4× in this paper · explained in 13 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Objective Function — 1× in this paper · explained in 2 episodes

Sources

• Distinguishability and Accessible Information in Quantum Theory
• Proof of the Orthogonal Measurement Conjecture for Qubit States
• A quantum version of randomization criterion
• Reverse Test and Characterization of Quantum Relative Entropy
• An example of a quantum statistical model which cannot be mapped to a less informative one by any trace preserving positive map
• On the condition of conversion of classical probability distribution families into quantum families
• An information-theoretic treatment of quantum dichotomies
• Resource theory of asymmetric distinguishability

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