Effective size of certain macroscopic quantum superpositions -: art. no. 210402

Several experiments and experimental proposals for the production of macroscopic superpositions naturally lead to states of the general form \phi(1)](xN) + \phi(2)](xN), where the number of subsystems N is very large, but the states of the individual subsystems have large overlap, \[phi(1)\phi(2)]\(2) = 1 - epsilon(2). We propose two different methods for assigning an effective particle number to such states, using ideal Greenberger-Horne-Zeilinger states of the form \0](xn) + \1](xn) as a standard of comparison. The two methods are based on decoherence and on a distillation protocol, respectively. Both lead to an effective size n of the order of N epsilon(2).