Quantum Correlations for Computation

Quantum Correlations for Computation

Seminar author:Jelena Mackeprang

Event date and time:02/10/2022 04:00:pm

Event location:

Event contact:

Non-adaptive measurement based quantum computation (NMQC) is a type of quantum computation where quantum non-locality is used as a resource. In an NMQC procedure the goal is to compute a multivariate function over a finite field. Its success is closely related to the violation of a (generalised) Bell inequality. NMQC can thus be used as an information theoretical tool to generate new findings on Bell inequalities and non-locality in general. In this talk, I discuss its generalised version with qu-d-its. More precisely, I consider qutrit NMQC and show that the generalised qutrit Greenberger-Horne-Zeilinger (GHZ) state enables the deterministic computation of all multivariate functions over the finite field of order three. This means that for any multivariate ternary function, there exists a generalised Bell inequality whose quantum violation is maximal. I also provide an example for an n-variate ternary function that can be computed with only n + 1 qutrits. To demonstrate that not all functions can be computed efficiently with qutrit NMQC and the qutrit GHZ state, I find a family of functions whose deterministic computation with the qutrit GHZ state requires an exponentially growing number of qutrits.