The power of qutrits for nonadaptive measurementbased quantum computing
Abstract
Nonlocality is not only one of the most prominent quantum features but can also serve as a resource for various informationtheoretical tasks. Analysing it from an informationtheoretical perspective has linked it to applications such as nonadaptive measurementbased 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 $2^n1$ 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 threevalued logic functions using the generalised qutrit GreenbergerHorneZeilinger (GHZ) state as a resource and at most $3^n1$ qutrits. This yields a corresponding generalised GHZ type paradox for any threevalued logic function that LHVs cannot compute. We give an example for an nvariate 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.
 Publication:

New Journal of Physics
 Pub Date:
 July 2023
 DOI:
 10.1088/13672630/acdf77
 arXiv:
 arXiv:2203.12411
 Bibcode:
 2023NJPh...25g3007M
 Keywords:

 quantum information;
 quantum computing;
 quantum correlations;
 Bell inequalities;
 Quantum Physics
 EPrint:
 New Journal of Physics 25, 073007 (2023)