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Pairwise Concurrence Dynamics in a Five Qubit Model

Seyed Arash Ghoreishi

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

In this paper, we study the entanglement in a five qubit model. For this purpose, we consider two non-interacting systems A and B which are correlated together initially. A is a t wo atoms Tavis-Cu mmings system and B is a Jaynes-Cummings System. By choosing a convenient initial condition which shows the initially correlation, our total system (A plus B) become a system which consist of five qubits. There are ten pairwise concurrences which we must calculate. We show that initially non-entangled qubits become entangled by passing time, the process which may be interpreted as entanglement transfer. We also show that our model in special cases become two-qubit and three-qubit models and analyze entanglement in these special cases.

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In this paper, we study the entanglement in a five qubit model. For this purpose, we consider two non-interacting systems A and B which are correlated together initially. A is a t wo atoms Tavis-Cu mmings system and B is a Jaynes-Cummings System. By choosing a convenient initial condition which shows the initially correlation, our total system (A plus B) become a system which consist of five qubits. There are ten pairwise concurrences which we must calculate. We show that initially non-entangled qubits become entangled by passing time, the process which may be interpreted as entanglement transfer. We also show that our model in special cases become two-qubit and three-qubit models and analyze entanglement in these special cases.
We consider two non interacting two-atoms Tavis-Cummings systems and examine the entanglement among four two-state atoms. For our purpose, we assume that one atom from each system are entangled initially and we obtain time-dependent concurrence among atoms. There are six pairwise concurrences among atoms and in this paper, we focus on remote atoms. We show that initially non-entangled atoms and becomes entangled by passing time, the process which may be interpreted as entanglement transfer between the cavities.
A detailed treatment of the entanglement dynamics of two distant but non-identical systems is presented. We study the entanglement evolution of two remote atoms interacting independently with a cavity field, as in the double Jaynes–Cummings model. The four-qubit pairwise concurrences are studied, allowing for asymmetric atom–cavity couplings and off-resonant interactions. Counter to intuition, imperfect matching can prove advantageous to entanglement creation and evolution. For two types of initial entanglement, corresponding to spin-correlated and anti-correlated Bell states Φ and Ψ, a full, periodic and directed transfer of entanglement into a specific qubit pair is possible, for resonant interactions, depending on the choice of relative couplings. Furthermore, entanglement transfer and sudden death (ESD) can be prevented using off-resonant interactions, although for some initial states, detunings will trigger an otherwise frozen entanglement, to allow a full entanglement transfer.
We examine entanglement dynamics via concurrence among four two-state systems labelled A , a , B , b . The four systems are arranged on an addressable 'lattice' in such a way that A and a at one location labelled Aa can interact with each other via excitation exchange, and the same for B and b at location Bb . The Aa location is prepared entangled with the Bb location, but their mutual complete isolation prevents interaction in the interval between actions of an external addressing agent. There are six pairwise concurrences on the lattice, and we follow their evolution in the interval between external actions. We show how entanglement evolves and may exhibit the non-analytic effect termed entanglement sudden death (ESD), with periodic recovery. These loss and gain processes may be interpreted as entanglement transfers between the subsystems.
Abstract In this paper, we investigate the dynamics and transfer of multipartite entanglement via concurrence and three-tangle in a double and a triple Tavis–Cummings model (TCM). The results are compared with those of the double and triple Jaynes–Cummings model (JCM). We find that the dynamics and transfer of multipartite entanglement are dependent only on the initial entanglement type itself and not on model type for the double and triple TCM. For the triple TCM and the triple JCM we find that entanglement of a different type from the initial entanglement is created. Our work will further enrich the previous results for the JCM and the TCM.
We consider an entangled but non-interacting qubit pair a 1 and b 1 that is independently coupled to a set of local qubit systems, a I and b J , of 0 bit value, respectively. We derive rules for the transfer of entanglement from the pair a 1 – b 1 to an arbitrary pair a I – b J , for the case of qubit-number conserving local interactions. It is shown that the transfer rule depends strongly on the initial entangled state. If the initial entanglement is in the form of the Bell state corresponding to anti-correlated qubits, the sum of the square of the nonlocal pairwise concurrences is conserved. If the initial state is the Bell state with correlated qubits, this sum can be reduced, even to zero in some cases, to reveal a complete and abrupt loss of all nonlocal pairwise entanglement. We also identify that for the nonlocal bipartitions A – b J involving all qubits at one location, with one qubit b J at the other location, the concurrences satisfy a simple addition rule for both cases of the Bell states that the sum of the square of the nonlocal concurrences is conserved.
Motivated by recent experimental studies on coherent dynamics transfer in three interacting atoms or electron spins [Phys. Rev. Lett 114 (2015) 113002, Phys. Rev. Lett 120 (2018) 243604], here we study entanglement entropy transfer in three interacting qubits. We analytically calculate time evolutions of wave function, density matrix and entanglement of the system. We find that initially entangled two qubits may alternatively transfer their entanglement entropy to other two qubit pairs. Thus dynamical evolution of three interacting qubits may produce a genuine three-partite entangled state through entanglement entropy transfers. In particular, different pairwise interactions of the three qubits endow symmetric and asymmetric evolutions of the entanglement transfer, characterized by the quantum mutual information and concurrence. Finally, we discuss an experimental proposal of three Rydberg atoms for testing the entanglement dynamics transfer of this kind .