# An operator-algebraic formulation of self-testing

### APA

Paul-Paddock, C. (2022). An operator-algebraic formulation of self-testing. Perimeter Institute. https://pirsa.org/22110100

### MLA

Paul-Paddock, Connor. An operator-algebraic formulation of self-testing. Perimeter Institute, Nov. 16, 2022, https://pirsa.org/22110100

### BibTex

@misc{ pirsa_PIRSA:22110100, doi = {10.48660/22110100}, url = {https://pirsa.org/22110100}, author = {Paul-Paddock, Connor}, keywords = {Quantum Information}, language = {en}, title = {An operator-algebraic formulation of self-testing}, publisher = {Perimeter Institute}, year = {2022}, month = {nov}, note = {PIRSA:22110100 see, \url{https://pirsa.org}} }

Connor Paul-Paddock University of Waterloo

## Abstract

We give a new definition of self-testing for correlations in terms of states on C*-algebras. We show that this definition is equivalent to the standard definition for any class of finite-dimensional quantum models which is closed under submodels and direct sums, provided that the correlation is extremal and has a full-rank model in the class. This last condition automatically holds for the class of POVM quantum models, but does not necessarily hold for the class of projective models by a result of Mancinska and Kaniewski. For extremal binary correlations and for extremal synchronous correlations, we show that any self-test for projective models is a self-test for POVM models. The question of whether there is a self-test for projective models which is not a self-test for POVM models remains open. An advantage of our new definition is that it extends naturally to commuting operator models. We show that an extremal correlation is a self-test for finite-dimensional quantum models if and only if it is a self-test for finite-dimensional commuting operator models, and also observe that many known finite-dimensional self-tests are in fact self-tests for infinite-dimensional commuting operator models.

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