Bell numbers and coherent states

K. A. Penson, A. I. Solomon

Conventional Bell and Stirling numbers arise naturally in the normal ordering of simple monomials in boson operators. By extending this process we obtain generalizations of these combinatorial numbers, defined as coherent state matrix elements of arbitrary monomials, as well as the associated Dobinski relations. These Bell-type numbers may be considered as power moments and give rise to positive measures which allow the explicit construction of new classes of coherent states.

Yoshio Ohnuki, S. Kamefuchi

Zhang Guo

Interaction between two atoms is considered.The fidelities of quantum states in the system of the two-mode entangled coherent field interacting with atoms in Bell states are derived.The results indicate that for ideal cavity,the fidelity of the system always equals to one for the coherent maintenance state at original time.The fidelities of the system surge periodically from 0 to 1 for the etceteras Bell state at original time when average photon number of two-mode entangled coherent states cavity fields are very small.When average photon number of two-mode entangled coherent states cavity fields increase,oscillatory frequency of the fidelities of the system augments and swing decrease.For fine cavity,the fidelity of the system is humdrum exponent attenuation for the coherent maintenance state at original time.The fidelities of the system are oscillatory exponent attenuation for the etceteras Bell state at original time,and when average photon number of two-mode entangled coherent states cavity fields increase,oscillatory frequency of the fidelities of the system augments and swing decrease.

Jean-Pierre Antoine, Bagarello, Fabio, Jean‐Pierre Gazeau

Akira Kitagawa, Katsuji Yamamoto

We analyze the linear optical realization of number-sum Bell measurement and number-state manipulation by taking into account the realistic experimental situation, specifically imperfectness of single-photon detector. The present scheme for number-state manipulation is based on the number-sum Bell measurement, which is implemented with linear optical elements, i.e., beam splitters, phase shifters, and zero-one-photon detectors. Squeezed vacuum states and coherent states are used as optical sources. The linear optical Bell state detector is formulated quantum theoretically with a probability operator measure. Then, the fidelity of manipulation and preparation of number states, particularly for qubits and qutrits, is evaluated in terms of the quantum efficiency and dark count of single-photon detector. It is found that a high fidelity is achievable with small enough squeezing parameters and coherent state amplitudes.

Tatyana Barron, Alexander Kazachek