An analysis of the Spekkens toy theory with connection to Wootters discrete phase space
The toy model of Spekkens is a formalism which can partially describe quantum mechanics. The theory deals with the (epistemic) states of a spin-1/2 particle, or qubits and it is closely related to the discrete phase space formalism of Wootters and collaborators. One can apply the stabilizer formalis...
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| Format: | Article |
| Language: | English |
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Institute of Physics Publishing
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/36386/ http://psasir.upm.edu.my/id/eprint/36386/1/An%20analysis%20of%20the%20Spekkens%20toy%20theory%20with%20connection%20to%20Wootters%20discrete%20phase%20space.pdf |
| _version_ | 1848848317822271488 |
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| author | Aliakbarzadeh, Mojtaba Zainuddin, Hishamuddin |
| author_facet | Aliakbarzadeh, Mojtaba Zainuddin, Hishamuddin |
| author_sort | Aliakbarzadeh, Mojtaba |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The toy model of Spekkens is a formalism which can partially describe quantum mechanics. The theory deals with the (epistemic) states of a spin-1/2 particle, or qubits and it is closely related to the discrete phase space formalism of Wootters and collaborators. One can apply the stabilizer formalism for finding similarities of these two models. Noting that MUB basis vectors are obtained by eigenstates of generalized Pauli operators, the MUB basis vectors are thus the set of stabilizer states. Galvao has characterized the set of states with non-negative Wigner function class; they form the convex hull of the stabilizer states used as the MUB basis vectors. By combining both approaches, one can show epistemic states that are analogous to the convex hull of the stabilizer states (used as basis vectors in the MUB set) always make valid nonmaximal knowledge epistemic states. |
| first_indexed | 2025-11-15T09:32:35Z |
| format | Article |
| id | upm-36386 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:32:35Z |
| publishDate | 2014 |
| publisher | Institute of Physics Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-363862015-12-01T03:41:17Z http://psasir.upm.edu.my/id/eprint/36386/ An analysis of the Spekkens toy theory with connection to Wootters discrete phase space Aliakbarzadeh, Mojtaba Zainuddin, Hishamuddin The toy model of Spekkens is a formalism which can partially describe quantum mechanics. The theory deals with the (epistemic) states of a spin-1/2 particle, or qubits and it is closely related to the discrete phase space formalism of Wootters and collaborators. One can apply the stabilizer formalism for finding similarities of these two models. Noting that MUB basis vectors are obtained by eigenstates of generalized Pauli operators, the MUB basis vectors are thus the set of stabilizer states. Galvao has characterized the set of states with non-negative Wigner function class; they form the convex hull of the stabilizer states used as the MUB basis vectors. By combining both approaches, one can show epistemic states that are analogous to the convex hull of the stabilizer states (used as basis vectors in the MUB set) always make valid nonmaximal knowledge epistemic states. Institute of Physics Publishing 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/36386/1/An%20analysis%20of%20the%20Spekkens%20toy%20theory%20with%20connection%20to%20Wootters%20discrete%20phase%20space.pdf Aliakbarzadeh, Mojtaba and Zainuddin, Hishamuddin (2014) An analysis of the Spekkens toy theory with connection to Wootters discrete phase space. Journal of Physics: Conference Series, 553. art. no. 012008. pp. 1-6. ISSN 1742-6588; ESSN: 1742-6596 http://iopscience.iop.org/article/10.1088/1742-6596/553/1/012008/meta 10.1088/1742-6596/553/1/012008 |
| spellingShingle | Aliakbarzadeh, Mojtaba Zainuddin, Hishamuddin An analysis of the Spekkens toy theory with connection to Wootters discrete phase space |
| title | An analysis of the Spekkens toy theory with connection to Wootters discrete phase space |
| title_full | An analysis of the Spekkens toy theory with connection to Wootters discrete phase space |
| title_fullStr | An analysis of the Spekkens toy theory with connection to Wootters discrete phase space |
| title_full_unstemmed | An analysis of the Spekkens toy theory with connection to Wootters discrete phase space |
| title_short | An analysis of the Spekkens toy theory with connection to Wootters discrete phase space |
| title_sort | analysis of the spekkens toy theory with connection to wootters discrete phase space |
| url | http://psasir.upm.edu.my/id/eprint/36386/ http://psasir.upm.edu.my/id/eprint/36386/ http://psasir.upm.edu.my/id/eprint/36386/ http://psasir.upm.edu.my/id/eprint/36386/1/An%20analysis%20of%20the%20Spekkens%20toy%20theory%20with%20connection%20to%20Wootters%20discrete%20phase%20space.pdf |