Displaced rotations of coherent states

Sergey A. Podoshvedov

We propose an approach that enables to use it for construction of rotations of coherent states, in particular, it gives a possibility to construct Hadamard gate for the 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. Studied optical scheme is based on alternation of photon additions and displacement operators (in general case, photon additions and displacements are required) with seed coherent state to generate both even and odd displaced squeezed SCSs (DSSCSs) regardless of number of used photon additions. It is shown the studied optical scheme is sensitive to seed coherent state provided that other parameters 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 rotation operator 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.

Luciano Fonda, N. Mankoč-Borštnik, Mitja Rosina

Sergey A. Podoshvedov

We study the method of generation of states that approximate superpositions of large-amplitude coherent states (SCSs) with high fidelity in free-traveling fields. Our approach is based on the representation of an arbitrary single-mode pure state, and SCSs in particular, in terms of displaced number states with an arbitrary displacement amplitude. The proposed optical scheme is based on alternation of photon additions and displacement operators (in the general case, N photon additions and N − 1 displacements are required) with a seed coherent state to generate both even and odd displaced squeezed SCSs regardless of the parity of the used photon additions. It is shown that the optical scheme studied is sensitive to the seed coherent state if the other parameters are unchanged. Output states can approximate either even squeezed SCS or odd SCS shifted relative to each other by some value. This allows constructing a local rotation operator, in particular, the Hadamard gate, which is a mainframe element for quantum computation with coherent states. We also show that three-photon additions with two intermediate displacement operators are sufficient to generate even displaced squeezed SCS with the amplitude 1.7 and fidelity more than 0.99. The effects deteriorating the quality of output states are considered.

N. Mankoč-Borštnik

Blagovest A. Nikolov, D. A. Trifonov

A. Lukš, Vlasta Peřinová, J. Křepelka

The number-quadrature minimum-uncertainty states after rotation and displacement emerge in the parametric down-conversion followed by photon number measurement in the idler mode when the coherent state inputs. Again, the state generated in the signal mode by the reduction is described by the principally measurable quantum-statistical tools.