Displaced rotations of coherent states

We propose an approach with displaced states that can be used for rotations of coherent states. Our approach is based on representation of arbitrary one-mode pure state in free-travelling fields, in particular superposition of coherent states (SCSs), in terms of displaced number states with arbitrary amplitude of displacement. Optical scheme is developed for construction of displacing Hadamard gate for the coherent states. It is based on alternation of single photon additions and displacement operators (in general case, N-singe photon additions and N ? 1-displacements are required) with seed coherent state to generate both even and odd displaced squeezed SCSs regardless of number of used photon additions. The optical scheme is sensitive to the seed coherent state provided that other parameters of the scheme are invariable. Output states approximate with high fidelity either even squeezed SCS or odd SCS shifted relative each other by some value. It enables to construct local rotations for coherent states, in particular, Hadamard gate being mainframe element for quantum computation with coherent states. The effects deteriorating quality of output states are considered.