Quantum metrology with Fock and even coherent states: Parity detection approaches to the Heisenberg limit

Using an any number of photons Fock state |m〉|m〉 and an even coherent state as inputs of Mach–Zenhder interferometer (MZI), we investigate the quantum interference of output port on the basis of phase space theory. The statistical properties are discussed by explicitly deriving the Wigner function, photon-number distribution at individual output port. Moreover, the phase estimation is examined. It is shown that the parity signal is more super-resolved with the increase of m, nc values (nc is the square of amplitude of coherent state). The phase sensitivity has superior sensitivity in the vicinity of zero phase difference, and reaches below shot-noise limit when m≥1m≥1. It also approaches the Heisenberg limit with the increasing m.