Generation of arbitrary symmetric entangled states with conditional linear optical coupling

Abstract

An approach to generating the entangled photonic states $|{\ensuremath{\Psi}}_{1},{\ensuremath{\Psi}}_{2}\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|{\ensuremath{\Psi}}_{2},{\ensuremath{\Psi}}_{1}\ensuremath{\rangle}$ from two arbitrary states $|{\ensuremath{\Psi}}_{1}\ensuremath{\rangle}$ and $|{\ensuremath{\Psi}}_{2}\ensuremath{\rangle}$ is proposed. The protocol is implemented by the conditionally induced beam-splitter coupling, which leads to the selective swapping between two photonic modes. Such coupling occurs in a quantum system prepared in the superposition of two ground states with only one of them being involved in the swapping. All the entangled states in the category, such as entangled pairs of coherent states or Fock states (NOON states), can be efficiently produced in the same way by this method.