arXiv
Open Access
2021
Shannon capacity, Chess, DNA and Umbrellas
Oliver Knill
Abstrak
A vexing open problem in information theory is to find the Shannon capacity of odd cyclic graphs larger than the pentagon and especially for the heptagon. Lower bounds for the capacity are obtained by solving King chess puzzles. Upper bounds are obtained by solving entanglement problems, that is to find good Lovasz umbrellas, quantum state realizations of the graph. We observe that optimal states are always pure states. The rest is expository. One general interesting question is whether the Shannon capacity is always some n-th root of the independence number of the n'th power of the graph.
Topik & Kata Kunci
Penulis (1)
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Oliver Knill
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2021
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓