Engineering Yang-Lee anyons via Majorana bound states

We propose the platform of a Yang-Lee anyon system which is constructed from Majorana bound states in topological superconductors. Yang-Lee anyons, described by the nonunitary conformal field theory with the central charge c=-22/5, are nonunitary counterparts of Fibonacci anyons, obeying the same fusion rule but exhibiting nonunitary non-Abelian braiding statistics. We consider a topological superconductor junction system coupled with dissipative electron baths, which realizes a non-Hermitian interacting Majorana system. Numerically estimating the central charge, we examine the condition that the non-Hermitian Majorana system can simulate the Ising spin model of the Yang-Lee edge singularity and confirm that by controlling model parameters in a feasible way the Yang-Lee edge criticality is realized. On the basis of this scenario, we present a scheme for the fusion, measurement, and braiding of Yang-Lee anyons in our proposed setup.