PIRSA:21050020

The Stabilizer Subtheory Has a Unique Noncontextual Model

APA

Schmid, D. (2021). The Stabilizer Subtheory Has a Unique Noncontextual Model. Perimeter Institute for Theoretical Physics. https://pirsa.org/21050020

MLA

Schmid, David. The Stabilizer Subtheory Has a Unique Noncontextual Model. Perimeter Institute for Theoretical Physics, Jun. 01, 2021, https://pirsa.org/21050020

BibTex

          @misc{ scivideos_PIRSA:21050020,
            doi = {10.48660/21050020},
            url = {https://pirsa.org/21050020},
            author = {Schmid, David},
            keywords = {Quantum Foundations},
            language = {en},
            title = {The Stabilizer Subtheory Has a Unique Noncontextual Model},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2021},
            month = {jun},
            note = {PIRSA:21050020 see, \url{https://scivideos.org/index.php/pirsa/21050020}}
          }
          

David Schmid Perimeter Institute for Theoretical Physics

Talk numberPIRSA:21050020
Source RepositoryPIRSA
Collection

Abstract

We give a complete characterization of the (non)classicality of all stabilizer subtheories. First, we prove that there is a unique nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory in all odd dimensions, namely Gross’s discrete Wigner function. This representation is equivalent to Spekkens’ epistemically restricted toy theory, which is consequently singled out as the unique noncontextual ontological model for the stabilizer subtheory. Strikingly, the principle of noncontextuality is powerful enough (at least in this setting) to single out one particular classical realist interpretation. Our result explains the practical utility of Gross’s representation, e.g. why (in the setting of the stabilizer subtheory) negativity in this particular representation implies generalized contextuality, and hence sheds light on why negativity of this particular representation is a necessary resource for universal quantum computation in the state injection model. This last fact, together with our result, implies that generalized contextuality is also a necessary resource for universal quantum computation in this model. In all even dimensions, we prove that there does not exist any nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory, and, hence, that the stabilizer subtheory is contextual in all even dimensions.