A minimal completion theorem and almost everywhere equivalence for Completely Positive maps
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911887583608832 |
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| author | Bhat, B. V. Rajarama Chongdar, Arghya |
| author_facet | Bhat, B. V. Rajarama Chongdar, Arghya |
| contents | A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some very general conditions a completely positive map almost everywhere equivalent to a quasi-pure map is actually equal to that map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15952 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A minimal completion theorem and almost everywhere equivalence for Completely Positive maps Bhat, B. V. Rajarama Chongdar, Arghya Operator Algebras Quantum Physics 47A20, 46L53, 81P16, 81P47 A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some very general conditions a completely positive map almost everywhere equivalent to a quasi-pure map is actually equal to that map. |
| title | A minimal completion theorem and almost everywhere equivalence for Completely Positive maps |
| topic | Operator Algebras Quantum Physics 47A20, 46L53, 81P16, 81P47 |
| url | https://arxiv.org/abs/2306.15952 |