Catani, L;
Browne, DE;
de Silva, N;
(2019)
Spekkens’ toy model and contextuality as a resource in quantum computation.
In:
Foundations of Quantum Theory.
(pp. pp. 301-308).
IOS Press
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Abstract
Spekkens’ toy model (SM) is a non-contextual hidden-variable model made to support the epistemic view of quantum theory, where quantum states are states of partial knowledge about a deeper underlying reality. Despite being a classical model, it has reproduced many features of quantum theory (entanglement, teleportation, . . .): (almost) everything but contextuality, which therefore seems to be the inherent quantum feature. In addition to the importance in foundation of quantum theory, the notion of contextuality seems to be a crucial resource for quantum computation. In particular it has been proven that, in the case of odd prime discrete dimensional systems, contextuality is necessary for universal quantum computation in state-injection schemes of computation based on stabilizer quantum mechanics (SQM). The latter is a subtheory of quantum mechanics which is very popular in the field of quantum computation and quantum error correction. State-injection schemes consist of a classically-simulable part (like SQM) and a resource state that boosts the computation to a quantum improvement. In the odd-dimensional case, SM is operationally equivalent to SQM. In the even-dimensional case, the equivalence only holds in terms of structure, not in terms of statistical predictions. This because qubit-SQM shows contextuality, while qudit(odd dimensions)-SQM does not. We believe that SM can be a valid tool to study contextuality as a resource in the field of quantum computation. Restricted versions of SM compatible with quantum mechanics (QM) can be used as the non-contextual classically-simulable part of state-injection schemes thus opening other scenarios where studying if contextuality is necessary for quantum computational speed-up.
| Type: | Proceedings paper |
|---|---|
| Title: | Spekkens’ toy model and contextuality as a resource in quantum computation |
| ISBN-13: | 9781614999362 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.3254/978-1-61499-937-9-301 |
| Publisher version: | https://doi.org/10.3254/978-1-61499-937-9-301 |
| Language: | English |
| Additional information: | This is the published version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| 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-pp.ucl.ac.uk/id/eprint/10078314 |
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