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Smallest output dimension for a minimum-output-entropy violation

Find the smallest output dimension in which two quantum channels violate additivity of minimum output entropy; it lies between 2 and 182.

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1{
2 "domain": "physics-astronomy",
3 "topics": [
4 "quantum-information",
5 "mathematical-physics"
6 ],
7 "type": "construction",
8 "also": [
9 "proof"
10 ],
11 "source": {
12 "key": "qiqcop",
13 "name": "QIQCOP Zoo",
14 "url": "https://qiqc-op.com/problem/op_e724615844c52297/",
15 "id": "op_e724615844c52297",
16 "curator": "Bikun Li, Qicheng Tang, Changhao Li, Chengkai Zhu, Minbo Gao, Zhong-Xia Shang, Bin Cheng and Naixu Guo",
17 "poser": "QIQCOP Zoo contributors, after Belinschi, Collins and Nechita (2016)",
18 "status": "unsolved",
19 "as_of": "2026-10-20",
20 "catalog": "0521c19bbd38"
21 },
22 "review": true,
23 "approval": "first-time"
24}