No state-independent contextuality can be extracted from contextual measurement-based quantum computation with qudits of odd prime dimension

• URL: http://arxiv.org/abs/2209.14018v1
• Date: Wed, 28 Sep 2022 11:55:40 GMT
• Title: No state-independent contextuality can be extracted from contextual measurement-based quantum computation with qudits of odd prime dimension
• Authors: Markus Frembs, Cihan Okay, Ho Yiu Chung
• Abstract summary: Linear constraint systems (LCS) have proven to be a surprisingly prolific tool in the study of non-classical correlations. It is not known whether there exist LCS in odd dimension, which admit finite-dimensional quantum, but no classical solutions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Linear constraint systems (LCS) have proven to be a surprisingly prolific tool in the study of non-classical correlations and various related issues in quantum foundations. Many results are known for the Boolean case, yet the generalisation to systems of odd dimension is largely open. In particular, it is not known whether there exist LCS in odd dimension, which admit finite-dimensional quantum, but no classical solutions. Here, we approach this question from a computational perspective. We observe that every deterministic, non-adaptive measurement-based quantum computation (MBQC) with linear side-processing defines a LCS. Moreover, the measurement operators of such a MBQC almost define a quantum solution to the respective LCS: the only difference is that measurement operators generally only commute with respect to the resource state of the MBQC. This raises the question whether this state-dependence can be lifted in certain cases, thus providing examples of quantum solutions to LCS in odd dimension. Our main result asserts that no such examples arise within a large extension of the Pauli group for p odd prime, which naturally arises from and is universal for computation in deterministic, non-adaptive MBQC with linear side-processing.

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