Variations on the Choi-Jamiolkowski isomorphism
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866911991608639488 |
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| author | Frembs, Markus Cavalcanti, Eric G. |
| author_facet | Frembs, Markus Cavalcanti, Eric G. |
| contents | We address various aspects of a widely used tool in quantum information theory: the Choi-Jamiolkowski isomorphism [A. Jamiolkowski, Rep. Math. Phys., 3, 275 (1972)]. We review different versions of the isomorphism, their properties and propose a unified description that combines them all. To this end, we identify the physical reason for the appearance of the (basis-dependent) operation of transposition in the isomorphism as used in Choi's theorem [M.-D. Choi, Lin. Alg. Appl., 10, 285 (1975)]. This requires a careful distinction between Jordan algebras and the different C*-algebras they arise from, which are distinguished by their order of composition. Physically, the latter encodes a choice of time orientation in the respective algebras, which relates to a number of recent results, including a characterisation of quantum from more general non-signalling bipartite correlations [M. Frembs and A. Döring, arXiv:2204.11471] and a classification of bipartite entanglement [M. Frembs, arXiv:2207.00024]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_16533 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Variations on the Choi-Jamiolkowski isomorphism Frembs, Markus Cavalcanti, Eric G. Quantum Physics Mathematical Physics We address various aspects of a widely used tool in quantum information theory: the Choi-Jamiolkowski isomorphism [A. Jamiolkowski, Rep. Math. Phys., 3, 275 (1972)]. We review different versions of the isomorphism, their properties and propose a unified description that combines them all. To this end, we identify the physical reason for the appearance of the (basis-dependent) operation of transposition in the isomorphism as used in Choi's theorem [M.-D. Choi, Lin. Alg. Appl., 10, 285 (1975)]. This requires a careful distinction between Jordan algebras and the different C*-algebras they arise from, which are distinguished by their order of composition. Physically, the latter encodes a choice of time orientation in the respective algebras, which relates to a number of recent results, including a characterisation of quantum from more general non-signalling bipartite correlations [M. Frembs and A. Döring, arXiv:2204.11471] and a classification of bipartite entanglement [M. Frembs, arXiv:2207.00024]. |
| title | Variations on the Choi-Jamiolkowski isomorphism |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2211.16533 |