Gadget structures in proofs of the Kochen-Specker theorem
The Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned massive interest since its inception. We show that within every Kochen-Specker graph, there exist interesting subgraphs which we term $01$-gadgets, that capture the essential contradiction necessary to prove t...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2020-08-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2020-08-14-308/pdf/ |
| _version_ | 1811224113174282240 |
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| author | Ravishankar Ramanathan Monika Rosicka Karol Horodecki Stefano Pironio Michał Horodecki Paweł Horodecki |
| author_facet | Ravishankar Ramanathan Monika Rosicka Karol Horodecki Stefano Pironio Michał Horodecki Paweł Horodecki |
| author_sort | Ravishankar Ramanathan |
| collection | DOAJ |
| description | The Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned massive interest since its inception. We show that within every Kochen-Specker graph, there exist interesting subgraphs which we term $01$-gadgets, that capture the essential contradiction necessary to prove the Kochen-Specker theorem, i.e,. every Kochen-Specker graph contains a $01$-gadget and from every $01$-gadget one can construct a proof of the Kochen-Specker theorem. Moreover, we show that the $01$-gadgets form a fundamental primitive that can be used to formulate state-independent and state-dependent statistical Kochen-Specker arguments as well as to give simple constructive proofs of an ``extended'' Kochen-Specker theorem first considered by Pitowsky in \cite{Pitowsky}. |
| first_indexed | 2024-04-12T08:44:44Z |
| format | Article |
| id | doaj.art-1b7dc632292347b2b43daffcf75eb999 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-12T08:44:44Z |
| publishDate | 2020-08-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-1b7dc632292347b2b43daffcf75eb9992022-12-22T03:39:45ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2020-08-01430810.22331/q-2020-08-14-30810.22331/q-2020-08-14-308Gadget structures in proofs of the Kochen-Specker theoremRavishankar RamanathanMonika RosickaKarol HorodeckiStefano PironioMichał HorodeckiPaweł HorodeckiThe Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned massive interest since its inception. We show that within every Kochen-Specker graph, there exist interesting subgraphs which we term $01$-gadgets, that capture the essential contradiction necessary to prove the Kochen-Specker theorem, i.e,. every Kochen-Specker graph contains a $01$-gadget and from every $01$-gadget one can construct a proof of the Kochen-Specker theorem. Moreover, we show that the $01$-gadgets form a fundamental primitive that can be used to formulate state-independent and state-dependent statistical Kochen-Specker arguments as well as to give simple constructive proofs of an ``extended'' Kochen-Specker theorem first considered by Pitowsky in \cite{Pitowsky}.https://quantum-journal.org/papers/q-2020-08-14-308/pdf/ |
| spellingShingle | Ravishankar Ramanathan Monika Rosicka Karol Horodecki Stefano Pironio Michał Horodecki Paweł Horodecki Gadget structures in proofs of the Kochen-Specker theorem Quantum |
| title | Gadget structures in proofs of the Kochen-Specker theorem |
| title_full | Gadget structures in proofs of the Kochen-Specker theorem |
| title_fullStr | Gadget structures in proofs of the Kochen-Specker theorem |
| title_full_unstemmed | Gadget structures in proofs of the Kochen-Specker theorem |
| title_short | Gadget structures in proofs of the Kochen-Specker theorem |
| title_sort | gadget structures in proofs of the kochen specker theorem |
| url | https://quantum-journal.org/papers/q-2020-08-14-308/pdf/ |
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