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arXiv:quant-ph/0502008 · Physica Scripta

Dynamics of Tripartite Entanglement

S. Shelly Sharma, Naresh Kumar Sharma

Published Jan 1, 2005• 2 citations
arXivHTMLPDF

Abstract

Maximally entangled states are of utmost importance to quantum communication, dense coding, and quantum teleportation. With a trapped ion placed inside a high finesse optical cavity, interacting with field of an external laser and quantized cavity field, a scheme to generate a maximally entangled three qubit GHZ state, is proposed. The dynamics of tripartite entanglement is investigated, using negativity as an entanglement measure and linear entropy as a measure of mixedness of a state. It is found that (a) the number of modes available to the subsystem determines the maximum entanglement of a subsystem, (b) at entanglement maxima and minima, linear entropy and negativity uniquely determine the nature of state, but the two measures do not induce the same ordering of states, and (c) for a special choice of system parameters maximally entangled tripartite two mode GHZ state is generated. The scheme presented for GHZ state generation is a single step process and is reduction-free.

DOI
10.1238/physica.topical.118a00272

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Maximally entangled states are of utmost importance to quantum communication, dense coding, and quantum teleportation. With a trapped ion placed inside a high finesse optical cavity, interacting with field of an external laser and quantized cavity field, a scheme to generate a maximally entangled three qubit GHZ state, is proposed. The dynamics of tripartite entanglement is investigated, using negativity as an entanglement measure and linear entropy as a measure of mixedness of a state. It is found that (a) the number of modes available to the subsystem determines the maximum entanglement of a subsystem, (b) at entanglement maxima and minima, linear entropy and negativity uniquely determine the nature of state, but the two measures do not induce the same ordering of states, and (c) for a special choice of system parameters maximally entangled tripartite two mode GHZ state is generated. The scheme presented for GHZ state generation is a single step process and is reduction-free.
We investigate the non-dissipative decoherence of three qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Modelling the environment as a set of noninteracting harmonic oscillators, analytical expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state, and the population inversion have been obtained. The pointer observable is the energy of the isolated quantum system. Coupling to environment results in exponential decay of off diagonal matrix elements of the state operator with time as well as a phase decoherence of the component states. Numerical calculations to examine the time evolution of GHZ state generation probability and population inversion for different system environment coupling strengths are performed. Using negativity as an entanglement measure and linear entropy as a measure of mixedness, the entanglement dynamics of the tripartite system in the presence of decoherence is analysed.
We investigate the generation of tripartite field states inside the high-Q cavities using the cavity QED. The main goal is to successfully generate the entanglement in tripartite systems by passing two-level atoms through three identical high-Q cavities. Our scheme gives the successful generation of entangled tripartite W and GHZ states for pre-determined interaction times of atoms with the cavity fields. The dynamics of initial entangled states is studied as the system evolves in the dissipative environments.
A scheme to generate three qubit maximally entangled W-states, using three trapped ions interacting with the red sideband tuned single-mode field of a high finesse cavity, is proposed. For the cavity field initially prepared in a number state, the probability of generating the three-ion W-state is calculated. By using the ion-cavity coupling strengths achieved in experimental realizations, the interaction time needed for W-state generation is found to be of the order of 10 µs. It is found that for a fixed number of photons in the cavity the nature of entanglement of ionic internal states can be manipulated by an appropriate choice of the initial-state phonon number. The ionic qubits in the W-like state are found to be entangled to cavity photons. Analytical expressions for global negativity and partial K -way negativities ( K = 2 to 4) are obtained to study the evolution of entanglement distribution as a function of the interaction parameter. Reversible entanglement exchange between different entanglement modes is observed. For specific values of the interaction parameter, the three ions and photon–phonon system are found to have 4-partite entanglement, generated by 2-way and 3-way correlations.
Following a recent proposal ( Phys. Lett. A 346 (2005) 330) about quantum dense coding using a tripartite entangled GHZ state and W state, this paper proposes an experimentally feasible scheme for dense coding in cavity QED by using another peculiar tripartite entangled state. In the scheme the atoms interact simultaneously with a highly detuned cavity mode with the assistance of a classical field, the successful probability of dense coding scheme with this peculiar tripartite entangled state equals 1.
In this paper, we present a peculiar tripartite entangled state that is inequivalent to both the GHZ state and the W state, and then propose to implement efficient quantum information processing such as quantum dense coding and teleportation with this entangled state in cavity QED. In this scheme the atoms interact with a highly detuned cavity field with the assistance of a strong classical driven field. It does not require the transfer of quantum information between the atomic system and the cavity, and then our scheme is insensitive to both the cavity decay and the thermal field.
We numerically investigate the generation and dynamics of tripartite entanglement among qubits (quantum emitters or atoms) in multimode cavity quantum electrodynamics (cQED). Our cQED architecture features three initially unentangled excited two-level quantum emitters confined within a triangle-shaped multimode optical cavity, which later become entangled due to a Jaynes-Cummings-like interaction. Using the tripartite negativity measure of entanglement and fidelity with respect to the genuine tripartite entangled state (Greenberger-Horne-Zeilinger state, to be precise), we analyze the impact of the number of cavity modes, qubit locations, and losses (spontaneous emission from qubits and photon leakage from the cavity mirrors) on the generated entanglement. Our key results include the presence of two kinds of retardation effects: one resulting from the time it takes for photons to propagate from one qubit to another, and the other to complete one round trip in the cavity. We observed these retardation effects only in multimode cavities, with the exciting possibility of controlling the collapse and revival patterns of tripartite entanglement by altering the qubit locations in the cavity. Furthermore, the impact of losses on the generated entanglement and the dependence of maximum entanglement on the total number of modes yield results that surpass those reported for single and two excitations. With recent advances in circuit quantum electrodynamics, these findings hold promise for the development of entanglement-based quantum networking protocols and quantum memories.