No-broadcasting characterizes operational contextuality
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912702549458944 |
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| author | Jokinen, Pauli Weilenmann, Mirjam Plávala, Martin Pellonpää, Juha-Pekka Kiukas, Jukka Uola, Roope |
| author_facet | Jokinen, Pauli Weilenmann, Mirjam Plávala, Martin Pellonpää, Juha-Pekka Kiukas, Jukka Uola, Roope |
| contents | Operational contextuality forms a rapidly developing subfield of quantum information theory. However, the characterization of the quantum mechanical entities that fuel the phenomenon has remained unknown with many partial results existing. Here, we present a resolution to this problem by connecting operational contextuality one-to-one with the no-broadcasting theorem. The connection works both on the level of full quantum theory and subtheories thereof. We demonstrate the connection in various relevant cases, showing especially that for quantum states the possibility of demonstrating contextuality is exactly characterized by non-commutativity, and for measurements this is done by a norm-1 property closely related to repeatability. Moreover, we show how techniques from broadcasting can be used to simplify known foundational results in contextuality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | No-broadcasting characterizes operational contextuality Jokinen, Pauli Weilenmann, Mirjam Plávala, Martin Pellonpää, Juha-Pekka Kiukas, Jukka Uola, Roope Quantum Physics Operational contextuality forms a rapidly developing subfield of quantum information theory. However, the characterization of the quantum mechanical entities that fuel the phenomenon has remained unknown with many partial results existing. Here, we present a resolution to this problem by connecting operational contextuality one-to-one with the no-broadcasting theorem. The connection works both on the level of full quantum theory and subtheories thereof. We demonstrate the connection in various relevant cases, showing especially that for quantum states the possibility of demonstrating contextuality is exactly characterized by non-commutativity, and for measurements this is done by a norm-1 property closely related to repeatability. Moreover, we show how techniques from broadcasting can be used to simplify known foundational results in contextuality. |
| title | No-broadcasting characterizes operational contextuality |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.07305 |