text: The internal states of each ion can be treated as a two level system, with eigenstates denoted  and . One of the ion's normal modes is chosen to be the transfer mode used for state mapping. This motional mode must be shared by both ions, which requires both ions be similar in mass. The normal mode has harmonic oscillator states denoted as , where n is the nth level of mode m. The wave function
  denotes both ions and the transfer mode in the ground state. S and L represent the spectroscopy and logic ion. The spectroscopy ion's spectroscopy transition is then excited with a laser, producing the state:
  A red sideband pi-pulse is then driven on the spectroscopy ion, resulting in the state:
  At this stage, the spectroscopy ions internal state has been mapped on to the transfer mode. The internal state of the ion has been coupled to its motional mode. The  state is unaffected by the pulse of light carrying out this operation because the state  does not exist. QLS takes advantage of this in order to map the spectroscopy ions state onto the transfer mode. A final red sideband pi-pulse is applied to the logic ion, resulting in the state:
  The spectroscopy ion's initial state has been mapped onto the logic ion, which can then be detected.