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Conference Paper: Gadget Structures in Proofs of the Kochen-Specker Theorem
Title | Gadget Structures in Proofs of the Kochen-Specker Theorem |
---|---|
Authors | |
Issue Date | 2019 |
Citation | 3rd Workshop: Quantum Contextuality in Quantum Mechanics and Beyond (QCQMB), Prague, Czech Republic, 18-19 May 2019 How to Cite? |
Abstract | The Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned
massive interest since its inception. We show (in [1]) that within every Kochen-Specker graph,
there exist interesting subgraphs which we term 01-gadgets [2], 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
[3]. We conclude with some recent developments on the topic.
[1] R. Ramanathan, M. Rosicka, K. Horodecki, S. Pironio, M. Horodecki and P. Horodecki.
Gadget structures in proofs of the Kochen-Specker theorem. arXiv: 1807.00113 (2018).
[2] R. K. Clifton. Getting Contextual and Nonlocal Elements of Reality the Easy Way. American
Journal of Physics, 61: 443 (1993).
[3] I. Pitowsky. Infinite and finite Gleason’s theorems and the logic of indeterminacy. Journal
of Mathematical Physics 39, 218 (1998).
|
Description | Joint work with Monika Rosicka, Karol Horodecki, Stefano Pironio, Michał Horodecki, Paweł Horodecki |
Persistent Identifier | http://hdl.handle.net/10722/310692 |
DC Field | Value | Language |
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dc.contributor.author | Ramanathan, R | - |
dc.date.accessioned | 2022-02-10T03:33:03Z | - |
dc.date.available | 2022-02-10T03:33:03Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | 3rd Workshop: Quantum Contextuality in Quantum Mechanics and Beyond (QCQMB), Prague, Czech Republic, 18-19 May 2019 | - |
dc.identifier.uri | http://hdl.handle.net/10722/310692 | - |
dc.description | Joint work with Monika Rosicka, Karol Horodecki, Stefano Pironio, Michał Horodecki, Paweł Horodecki | - |
dc.description.abstract | The Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned massive interest since its inception. We show (in [1]) that within every Kochen-Specker graph, there exist interesting subgraphs which we term 01-gadgets [2], 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 [3]. We conclude with some recent developments on the topic. [1] R. Ramanathan, M. Rosicka, K. Horodecki, S. Pironio, M. Horodecki and P. Horodecki. Gadget structures in proofs of the Kochen-Specker theorem. arXiv: 1807.00113 (2018). [2] R. K. Clifton. Getting Contextual and Nonlocal Elements of Reality the Easy Way. American Journal of Physics, 61: 443 (1993). [3] I. Pitowsky. Infinite and finite Gleason’s theorems and the logic of indeterminacy. Journal of Mathematical Physics 39, 218 (1998). | - |
dc.language | eng | - |
dc.relation.ispartof | Workshop: Quantum Contextuality in Quantum Mechanics and Beyond (QCQMB) | - |
dc.title | Gadget Structures in Proofs of the Kochen-Specker Theorem | - |
dc.type | Conference_Paper | - |
dc.identifier.email | Ramanathan, R: ravi@cs.hku.hk | - |
dc.identifier.authority | Ramanathan, R=rp02582 | - |
dc.identifier.hkuros | 317354 | - |