Kostant relation in filtered randomized benchmarking for passive bosonic devices
Phys. Rev. A 113, 052602 – Published 4 May, 2026
DOI: https://doi.org/10.1103/xmlq-vssg
Abstract
We aim to reduce the cost of the current bosonic randomized benchmarking proposal. To do this, we introduce two filter functions: one uses immanants, the other uses characters of the special unitary group. These filters avoid computing Clebsch-Gordan (CG) coefficients and yield simple variance expressions. The character filter is not only efficient to compute, but also has a constant, low variance. Our filters rely on the same data as the original proposal. We also discuss an example with photon loss and gain. Our numerical evidence shows that a scheme using weak coherent states and intensity measurements can yield estimates close to those obtained without loss or gain. Our work could support simpler platform characterization and streamline data analysis.
