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

arXiv:2201.07611Physical Review AApr 4, 202220 citations

N

identical

d

-level systems to the dynamics of

d

bosonic modes with

N

particles, achieving an exponential reduction on the dimensionality of the problem in a simple and straightforward way. In particular, we consider the Lindblad dynamics of several identical multilevel systems interacting with a common subsystem under the action of collective dissipation terms.