  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 non-unitary conformal field theory with the central charge
$c=-22/5$, are non-unitary counterparts of Fibonacci anyons, obeying the same
fusion rule, but exhibiting non-unitary 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 the scheme for the fusion, measurement and braiding of
Yang-Lee anyons in our proposed setup.
