The Operational Choi–Jamiołkowski Isomorphism
In this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/9/1063 |
| _version_ | 1797552912851795968 |
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| author | Emily Adlam |
| author_facet | Emily Adlam |
| author_sort | Emily Adlam |
| collection | DOAJ |
| description | In this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi–Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations. |
| first_indexed | 2024-03-10T16:07:49Z |
| format | Article |
| id | doaj.art-95ff6d48c17b4a8db882bce78a2d96e6 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T16:07:49Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-95ff6d48c17b4a8db882bce78a2d96e62023-11-20T14:42:47ZengMDPI AGEntropy1099-43002020-09-01229106310.3390/e22091063The Operational Choi–Jamiołkowski IsomorphismEmily Adlam0Basic Research Community for Physics, 04315 Leipzig, GermanyIn this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi–Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.https://www.mdpi.com/1099-4300/22/9/1063quantum foundationsgeneralized probabilistic theoriesontologyquantum state |
| spellingShingle | Emily Adlam The Operational Choi–Jamiołkowski Isomorphism Entropy quantum foundations generalized probabilistic theories ontology quantum state |
| title | The Operational Choi–Jamiołkowski Isomorphism |
| title_full | The Operational Choi–Jamiołkowski Isomorphism |
| title_fullStr | The Operational Choi–Jamiołkowski Isomorphism |
| title_full_unstemmed | The Operational Choi–Jamiołkowski Isomorphism |
| title_short | The Operational Choi–Jamiołkowski Isomorphism |
| title_sort | operational choi jamiolkowski isomorphism |
| topic | quantum foundations generalized probabilistic theories ontology quantum state |
| url | https://www.mdpi.com/1099-4300/22/9/1063 |
| work_keys_str_mv | AT emilyadlam theoperationalchoijamiołkowskiisomorphism AT emilyadlam operationalchoijamiołkowskiisomorphism |