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Abstract
In this paper we construct a new type of finite-dimensional pair coherent states | ξ, q〉 as realizations of SU(2) Lie algebra. Using the technique of integration within an ordered product of operator, the nonorthogonality and completeness properties of the state | ξ, q〉 are investigated. Based on the Wigner operator in the entangled state | τ〉 representation, the Wigner function of | ξ, q〉 is obtained. The properties of | ξ, q〉 are discussed in terms of the negativity of its Wigner function. The tomogram of | ξ, q〉 is calculated with the aid of the Radon transform between the Wigner operator and the projection operator of the entangled state | η, κ 1, κ 2〉. In addition, using the entangled state | τ〉 representation of | ξ, q〉 to show that the states | ξ, q〉 are just a set of energy eigenstates of time-independent two coupled oscillators.
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