Single qubit operations with base squeezed coherent states

Liu He-sheng

Петер Адам, József Janszky

Sergey A. Podoshvedov

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.

Ma Shan-Jun

With a squeezing operation on the qubit state,we obtain a coherent superposition state of a squeezed vacuum state and a squeezed single photon state with certain weight rate.The coherent superposition state depends on the squeezing parameter and weight factor,I and its nonclassicality and non-Gaussian properties are researched.It is investigated by the sub-Poissonian statistics distribution of Mandel′s Q parameter and the negativity of the Wigner function.The non-Gaussianity of coherent superposition qubit state can be improved by adjusting the squeezing parameter and the weight factor.

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng

Sergey A. Podoshvedov

We develop a new method of representation of quantum states in terms of the displaced number states. We call it representation, where is an amplitude of the base displaced states. In particular, representation was obtained for set of the displaced number states with different amplitude of the displacement, two-mode squeezed vacuum (TMSV) and superposition of vacuum and single photon. The treatment is employed for building of elementary linear operators, in particular, two-qubit control-sign gate, Hadamard matrix between two two-dimensional Hilbert spaces. Main idea underlying the method is extraction of the displaced number state from initial state. Coherent qubit with large amplitude taken simultaneously two modes shifts two-mode target qubit on phase plane and constructive interference appears after measurement of single photon. The results are exact, any approximations are not exploited. We show implementation of the gates with almost unity fidelity of the output states is possible in realistic scenario.