When Complementary Measurements Count the Same Classical Bit Twice: Counterexamples to CQC, ECQC, and Complementarity-Based Certification

arXiv:2608.03828 · quant-ph, math-ph, math.MP · Submitted 2026-08-04 · Read on arXiv

quant-ph, math-ph, math.MP

Submitted: 2026-08-04

Updated: 2026-09-25

Comments: 9 pages. Updated the discussion to cite our companion paper arXiv:2608.04916, which proves CQC for all two-qubit states, and to clarify the sharp dimensional boundary. References updated. Results and proofs unchanged

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

Terminology

• Steering — 14× in this paper · explained in 2 episodes
• Entanglement — 7× in this paper · explained in 3 episodes
• Calibration — 3× in this paper · explained in 7 episodes
• Analyzer — 2× in this paper · explained in 1 episode
• Robustness — 2× in this paper · explained in 5 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Verifier — 1× in this paper · explained in 2 episodes

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