Catani, L;
Browne, DE;
(2017)
Spekkens' toy model in all dimensions and its relationship with stabiliser quantum mechanics.
New Journal of Physics
, 19
, Article 073035. 10.1088/1367-2630/aa781c.
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Abstract
Spekkens' toy model is a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is to advocate the epistemic view of quantum theory, where quantum states are states of incomplete knowledge about a deeper underlying reality. Many aspects of quantum mechanics and protocols from quantum information can be reproduced in the model. In spite of its significance, a number of aspects of Spekkens' model remained incomplete. Formal rules for the update of states after measurement had not been written down, and the theory had only been constructed for prime-dimensional and infinite dimensional systems. In this work, we remedy this, by deriving measurement update rules and extending the framework to derive models in all dimensions, both prime and non-prime. Stabiliser quantum mechanics (SQM) is a sub-theory of quantum mechanics with restricted states, transformations and measurements. First derived for the purpose of constructing error correcting codes, it now plays a role in many areas of quantum information theory. Previously, it had been shown that Spekkens' model was operationally equivalent to SQM in the case of odd prime dimensions. Here, exploiting known results on Wigner functions, we extend this to show that Spekkens' model is equivalent to SQM in all odd dimensions, prime and non-prime. This equivalence provides new technical tools for the study of technically difficult compound-dimensional SQM.
| Type: | Article |
|---|---|
| Title: | Spekkens' toy model in all dimensions and its relationship with stabiliser quantum mechanics |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1367-2630/aa781c |
| Publisher version: | https://doi.org/10.1088/1367-2630/aa781c |
| Language: | English |
| Additional information: | Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 Licence (http://creativecommons.org/licenses/by/3.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
| Keywords: | Spekkens' toy model, stabiliser quantum mechanics, discrete Wigner functions, non-prime dimensional systems, measurements update rules, epistemic view, contextuality |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1556720 |
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