Permutational symmetry for identical multilevel systems: A second-quantized approach

We develop a framework that provides straightforward approach to fully exploit the permutational symmetry of identical multilevel systems. By taking into account symmetry, we outline simple scheme allows us map dynamics $N$ $d$-level systems $d$ bosonic modes with particles, achieving an exponential reduction on dimensionality problem in and way. In particular, consider Lindblad several interacting common subsystem under action collective dissipation terms.