The power of qutrits for non-adaptive measurement-based quantum computing

Journal article

Non-locality is not only one of the most prominent quantum features but can also serve as a resource for various information-theoretical tasks. Analysing it from an information-theoretical perspective has linked it to applications such as non-adaptive measurement-based quantum computing (NMQC). In this type of quantum computing the goal is to output a multivariate function. The success of such a computation can be related to the violation of a generalised Bell inequality. So far, the investigation of binary NMQC with qubits has shown that quantum correlations can compute all Boolean functions using at most $2^n-1$ qubits, whereas local hidden variables (LHVs) are restricted to linear functions. Here, we extend these results to NMQC with qutrits and prove that quantum correlations enable the computation of all three-valued logic functions using the generalised qutrit Greenberger–Horne–Zeilinger (GHZ) state as a resource and at most $3^n-1$ qutrits. This yields a corresponding generalised GHZ type paradox for any three-valued logic function that LHVs cannot compute. We give an example for an n -variate function that can be computed with only n  + 1 qutrits, which leads to convenient generalised qutrit Bell inequalities whose quantum bound is maximal. Finally, we prove that not all functions can be computed efficiently with qutrit NMQC by presenting a counterexample

Authors: Mackeprang, J; Bhatti, D; Hoban, MJ; Barz, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: New Journal of Physics
• Volume: 25
• Issue: 7
• Pages: 073007-073007
• Publication date: 2023-06-19
• DOI: 10.1088/1367-2630/acdf77
• EISSN: 1367-2630
• ISSN: 1367-2630
• Language: English
• Keywords: Quantum; Counterexample; Quantum mechanics; Physics; Qubit; Quantum computer; Discrete mathematics; Mathematics; Quantum information; Qutrit