Abstract
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 XYZ 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.
Highlights
In this paper, motivated by the Möbius transformation and its action on symmetric points of the generalized circle in the complex plane, we introduce the complete set of spin-1/2 coherent states that are orthogonal and maximally entangled
We can interpret these quantum states as a qubit and its image state, realizing some kind of method of images in the quantum theory
In this paper we introduced the set of maximally entangled two- and three-qubit coherent states, determined by antipodal points on the Bloch sphere
Summary
If we consider two quantum states |ψi = ψ1 ψ2 and |wi = w1 w2 from 2D Hilbert space, related by a linear transformation |wi = U |ψi, it gives the fractional transformation (1) in the extended complex plane C. We fix ψ1 by the normalization condition hψ|ψi = 1, so that up to the global phase we have the qubit state as This state coincides with the spin-1/2 generalized coherent state [17]. The computational basis states |0i = |↑i = (1 0)T and |1i = |↓i = (0 1)T in this coherent state representation are given just by particular points in the extended complex plane (
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