Quantum counting algorithm and its application in mesoscopic physics

We discuss a quantum counting algorithm which transforms a physical particle-number state (and superpositions thereof) into a binary number. The algorithm involves two quantum Fourier transformations. One transformation is in physical space, where a stream of n<N=2^K (charged) particles is coupled to K qubits, rotating their states by prescribed angles. The second transformation is within the Hilbert space of qubits and serves to read out the particle number in a binary form. Applications include a divisibility check characterizing the size of a finite train of particles in a quantum wire and a scheme allowing one to entangle multiparticle wave functions in a Mach-Zehnder interferometer, generating Bell, Greenberger-Horne-Zeilinger, or Dicke states. ©2010 The American Physical Society