Faithful real embedding of a three-dimensional complex Kochen-Specker configuration
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909998595964928 |
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| author | Khrennikov, Andrei Svozil, Karl |
| author_facet | Khrennikov, Andrei Svozil, Karl |
| contents | We describe a phase-adjusted realification procedure that embeds any finite set of rays in C^3 into R^3. By assigning an appropriate phase to each ray before applying the standard coordinate-wise map, we can arrange that two rays are orthogonal in C^3 if and only if their images are orthogonal in R^6, so the construction yields a faithful orthogonal representation of the original complex configuration. As a concrete example, we consider the 165 projectively distinct rays used in a C^3 Kochen-Specker configuration obtained from mutually unbiased bases, list these 165 rays explicitly in C^3, and give for each of them its image in R^6 under the canonical realification map. We also note that, because the original 3-element contexts are no longer maximal in R^6, the embedded configuration admits two-valued states even though its realisation with maximal contexts in C^3 is Kochen-Specker uncolourable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17223 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Faithful real embedding of a three-dimensional complex Kochen-Specker configuration Khrennikov, Andrei Svozil, Karl Quantum Physics We describe a phase-adjusted realification procedure that embeds any finite set of rays in C^3 into R^3. By assigning an appropriate phase to each ray before applying the standard coordinate-wise map, we can arrange that two rays are orthogonal in C^3 if and only if their images are orthogonal in R^6, so the construction yields a faithful orthogonal representation of the original complex configuration. As a concrete example, we consider the 165 projectively distinct rays used in a C^3 Kochen-Specker configuration obtained from mutually unbiased bases, list these 165 rays explicitly in C^3, and give for each of them its image in R^6 under the canonical realification map. We also note that, because the original 3-element contexts are no longer maximal in R^6, the embedded configuration admits two-valued states even though its realisation with maximal contexts in C^3 is Kochen-Specker uncolourable. |
| title | Faithful real embedding of a three-dimensional complex Kochen-Specker configuration |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.17223 |