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Communications in Theoretical Physics

Three-Qubit Entanglement Sudden Death

Min Ge, Zhu Lin-Fan, Qiu Liang

Published Jun 1, 2008• 10 citations
Publisher

Abstract

We study entanglement dynamics of three-qubit system via negativity. Three atoms A, B, and C interact isolatedly with their own Jaynes–Cummings cavities a, b, and c. Aa system is prepared entangled with Bb and Cc, however, their mutual isolations forbid Aa interacting with system Bb and Cc. It is the same for system Bb and Cc. We show entanglement evolution of different three-qubit systems ABC, abc, Abc, and aBC and find entanglement sudden death effect.

DOI
10.1088/0253-6102/49/6/20

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We study entanglement dynamics of three-qubit system via negativity. Three atoms A, B, and C interact isolatedly with their own Jaynes–Cummings cavities a, b, and c. Aa system is prepared entangled with Bb and Cc, however, their mutual isolations forbid Aa interacting with system Bb and Cc. It is the same for system Bb and Cc. We show entanglement evolution of different three-qubit systems ABC, abc, Abc, and aBC and find entanglement sudden death effect.
In this article, we consider the entanglement between three identical qubits resonantly interacting with a thermal field of an Q-infinite resonator. We derived the exact solution of the evolution equation for density matrix of the considered system. On it basis we calculate the negativity as a criteria of entanglement between pairs of qubits for biseparable and entangled W-type states of qubits. The results showed that for considered initial qubits states the effect of the entanglement sudden death occurs for all values of the average number of thermal photons.
The article studies the dynamics of pairwise entanglement of three qubits, two of which are trapped in a resonator and interact with a single-mode ideal resonator through single-photon transitions, and the third qubit is outside the resonator. This takes into account the dipole-dipole coupling between the isolated qubit and the qubit in the resonator. We have found a solution to the quantum nonstationary Schrodinger equation for the total wave function of the system for the initial separable and biseparable states of qubits and the thermal initial state of the resonator field. Using these solutions, the criterion of entanglement of qubit pairs - negativity is calculated. The results of numerical simulation of the negativity criterion have shown that the including of a small dipole-dipole coupling between an isolated and one of the trapped qubits can lead to significant entanglement of qubit pairs for all initial states. There is a transition of entanglement from one pair of atoms to other pairs of atoms during the evolution of the system. It is also shown that for some separable and biseparable states, the dipole-dipole interaction can suppress the effect of sudden death of entanglement.
We study entanglement dynamics for a six-qubit model in cavity QED, where three two-level atoms A , B and C are initially prepared in a Greenberger–Horne–Zeilinger (GHZ)-like state and locally coupled with the independent cavities a , b and c , respectively. We consider entanglement evolution via negativity for the tripartite subsystems of atoms and the corresponding cavities. By choosing two types of GHZ-like states as atomic initial states, we shall show that the entanglement of atoms may or may not exhibit entanglement sudden death (ESD) depending on the type of atomic initial state.
In this work, we consider non-interacting atomic two level and three level (qubit-qutrit) systems interacting with a common environment in vacuum state. The interaction with the environment leads to the decoherece of the system due to spontaneous emission of atomic excited states which results in the decay of entanglement and other correlations of the qubit-qutrit system. We study the dynamics of entanglement for different initial class of states and negativity is used as a measure to quantify the degree of entanglement of qubit-qutrit system, the three level systems are considered in V configuration. We construct a class of rank dependant mixed boundary qubit-qutrit states as initial states. We observe entanglement sudden death for higher rank mixed boundary qubit-qutrit states.