Building of one-way Hadamard gate for squeezed coherent states

Abstract

We present an optical scheme to conditionally generate even or odd squeezed superpositions of coherent states (SSCSs). The optical setup consists of an unbalanced beam splitter whose transmittance tends to unity, and additional balanced beam splitters and photodetectors in auxiliary modes. Squeezed coherent states with different amplitudes are the input states in the optical scheme. The single-qubit operations are probabilistic and employ two- and three-photon subtractions from initial beams as the driving force. Generation of the even or odd SSCSs is observed in a wide diapason of values of used parameters. We consider a possibility to realize a one-way Hadamard gate for the squeezed coherent states when the base states are transformed into superposition states. States approximating the output states of a Hadamard gate with high fidelity can be realized by imposing restrictions on the values of used parameters. Higher-order subtractions from input beams are necessary to generate the SSCSs with larger amplitudes and higher fidelities. The problem is resolved in a Wigner representation to take into account imperfections of the optical devices. © 2013 American Physical Society.