Motivated by the Möbius transformation for symmetric points under the generalized circle in the complex plane, the system of symmetric spin coherent states corresponding to antipodal qubit states is introduced. In terms of these states, we construct the maximally entangled complete set of two-qubit coherent states, which in the limiting cases reduces to the Bell basis. A specific property of our symmetric coherent states is that they never become unentangled for any value of ψ from the complex plane. Entanglement quantifications of our states are given by the reduced density matrix and the concurrence determinant, and it is shown that our basis is maximally entangled. Universal one- and two-qubit gates in these new coherent state basis are calculated. As an application, we find the Q symbol of the XY Z model Hamiltonian operator H as an average energy function in maximally entangled two- and three-qubit phase space. It shows regular finite-energy localized structure with specific local extremum points. The concurrence and fidelity of quantum evolution with dimerization of double periodic patterns are given.
Motivated by Möbius transformation for symmetrical points under the generalized circle in complex plane, the system of symmetrical spin coherent states corresponding to antipodal qubit states is introduced. It implies the maximally entangled spin coherent states basis, which in the limiting cases reduces to the Bell basis. A specific property of our symmetric image coherent states is that they never become unentangled for any value of
ψ from complex plane. By the reduced density matrix and the concurrence determinant methods, it is shown that our basis is maximally entangled. In addition we find that the average of spin operators in these states vanish, as it must be according to another, operational definition of completely entangled states. Universal one qubit and two qubit gates in this new basis are calculated and time evolution of these states for some spin systems is derived. We find that the average energy for XYZ model in two qubit case (Q symbol of H) shows regular finite energy localized structure with characteristic extremum points, and appears as a soliton in maximally entangled two qubit phase space. Generalizations to three and higher qubit states are discussed.
The squeezing properties of a light-atom interacting system are studied by means of quantum theory. In the system, two two-level atoms are initially in an entangled state, and the coherent optical field is in a Schrodinger cat state. Influence of the strength of optical field and the phase angle of the coherent states on the double atoms dipole squeezing and the optical field amplitude squeezing are discussed by numerical calculations. It is found that under weak optical field condition, the optical field amplitude squeezing of even coherent state and Yurke-Stoler coherent state interacting with entangled state of atoms is no existence, but the optical field amplitude squeezing of odd coherent states is existence. In the same condition, the double atomic dipole squeezing of even coherent states interacting with entangled state of atoms is no existence, but the double atomic dipole squeezing of odd coherent state and Yurke-Stoler coherent state is existence. Under strong optical field condition, two squeezing phenomenon is no existence.