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International Journal of Theoretical Physics

New Maximally Entangled States for Pattern-Association Through Evolutionary Processes in a Two-Qubit System

Manu Pratap Singh, B. S. Rajput

Published Jan 14, 2017• 2 citations
Publisher
DOI
10.1007/s10773-016-3269-3

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New set of maximally entangled states (Singh-Rajput MES), constituting orthonormal eigen bases, has been revisited and its superiority and suitability in the processes of quantum associative memory (QuAM) have been demonstrated. Using these MES as memory states in the evolutionary process of pattern storage, the suitability and superiority of these MES over Bell’s MES have been demonstrated and it has been shown that, under the operations of all the possible memorization operators for a two-qubit system, the first two states of Singh-Rajput MES are useful for storing the pattern ǀ11 > and the last two of these MES are useful in storing the pattern ǀ10 > while Bell’s MES are not much suitable as memory states in a valid memorization process. Recall operations of quantum associate memory (QuAM) have been conducted through evolutionary process in terms of unitary operators by separately choosing Singh-Rajput MES and Bell’s MES as memory states for various queries and it has been shown that in each case the choices of Singh-Rajput MES as valid memory states are much more suitable than those of Bell’s MES.
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.