Tracially embeddable strategies: Lifting MIP* tricks to MIPco
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866908540225978368 |
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| author | Lin, Junqiao |
| author_facet | Lin, Junqiao |
| contents | We prove that any two-party correlation in the commuting operator model can be approximated using a tracially embeddable strategy, a class of strategies defined on a finite tracial von Neumann algebra, which we define in this paper. Using this characterization, we show that any approximately synchronous correlation can be approximated to the average of a collection of synchronous correlations in the commuting operator model. This generalizes the result from Vidick [JMP 2022] which only applies to finite-dimensional quantum correlations. As a corollary, we show that the quantum tensor code test from Ji et al. [FOCS 2022] follows the soundness property even under the general commuting operator model.
Furthermore, we extend the state-dependent norm variant of the Gowers-Hatami theorem to finite von Neumann algebras. Combined with the aforementioned characterization, this enables us to lift many known results about robust self-testing for non-local games to the commuting operator model, including a sample efficient finite-dimensional EPR testing for the commuting operator strategies. We believe that, in addition to the contribution from this paper, this class of strategies can be helpful for further understanding non-local games in the infinite-dimensional setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_01940 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tracially embeddable strategies: Lifting MIP* tricks to MIPco Lin, Junqiao Quantum Physics Operator Algebras We prove that any two-party correlation in the commuting operator model can be approximated using a tracially embeddable strategy, a class of strategies defined on a finite tracial von Neumann algebra, which we define in this paper. Using this characterization, we show that any approximately synchronous correlation can be approximated to the average of a collection of synchronous correlations in the commuting operator model. This generalizes the result from Vidick [JMP 2022] which only applies to finite-dimensional quantum correlations. As a corollary, we show that the quantum tensor code test from Ji et al. [FOCS 2022] follows the soundness property even under the general commuting operator model. Furthermore, we extend the state-dependent norm variant of the Gowers-Hatami theorem to finite von Neumann algebras. Combined with the aforementioned characterization, this enables us to lift many known results about robust self-testing for non-local games to the commuting operator model, including a sample efficient finite-dimensional EPR testing for the commuting operator strategies. We believe that, in addition to the contribution from this paper, this class of strategies can be helpful for further understanding non-local games in the infinite-dimensional setting. |
| title | Tracially embeddable strategies: Lifting MIP* tricks to MIPco |
| topic | Quantum Physics Operator Algebras |
| url | https://arxiv.org/abs/2304.01940 |