Energy localization in maximally entangled two- and three-qubit phase space

• Published in: New journal of physics Vol. 14; no. 6; pp. 63007 - 63030
• Main Authors: Pashaev, Oktay K, Gurkan, Zeynep N
• Format: Journal Article
• Language: English
• Published: IOP Publishing 07-06-2012
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/14/6/063007

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.