Evolution of tripartite entangled states in a decohering environment and their experimental protection using dynamical decoupling

Abstract

We embarked upon the task of experimental protection of different classes of tripartite entangled states, namely the maximally entangled GHZ and W states and the WW state, using dynamical decoupling. The states were created on a three-qubit NMR quantum information processor and allowed to evolve in the naturally noisy NMR environment. Tripartite entanglement was monitored at each time instant during state evolution, using negativity as an entanglement measure. It was found that the W state is most robust while the GHZ-type states are most fragile against the natural decoherence present in the NMR system. The WW state which is in the GHZ-class, yet stores entanglement in a manner akin to the W state, surprisingly turned out to be more robust than the GHZ state. The experimental data were best modeled by considering the main noise channel to be an uncorrelated phase damping channel acting independently on each qubit, alongwith a generalized amplitude damping channel. Using dynamical decoupling, we were able to achieve a significant protection of entanglement for GHZ states. There was a marginal improvement in the state fidelity for the W state (which is already robust against natural system decoherence), while the WW state showed a significant improvement in fidelity and protection against decoherence.

Control of the Geometric Phase in Two Open Qubit–Cavity Systems Linked by a Waveguide

“…To solve numerically the above differential equations in order to determine the wave function , we assume that the total system is initially in two different maximally entangled states: where we take the phase angle . The type of entanglement of the initial states of Equations (9) and (10) is very useful for distributed quantum information processing [ 29 , 30 , 31 ], and it possible to realize them experimentally [ 35 , 36 , 37 ].…”

Tripartite Entanglement: Foundations and Applications

“…The relationship between weak measurement and GHZ entanglement distribution in the presence of noise also it was investigated [218]. The robustness of GHZ and W states against decoherence it was experimentally investigated in [219]. In [220], it was presented a scheme for quantum communication in noisy environments by using a hybrid channel Bell-GHZ.…”

Maximum a posteriori probability estimates for quantum tomography

“…However most tomography setups have noise. For example, when discussing noise in a nuclear magnetic resonance (NMR) experiment [24][25][26] one may use the model described in Fig. 1, where the channel N , acting over time t represents the combined action of two channels, the generalized amplitude damping (T 1 ) channel,…”

“…The fidelity F(ρ,ρ) ≡ Tr( √ ρρ √ ρ) and trace distance D(ρ,ρ) ≡ 1 2 ||ρ −ρ|| 1 are, however popular choices. Various parameter choices for A and B are used in the simulation by fixing p = 1/2, T 1 /T 2 = 10 [26], t = kT 2 and varying k ∈ {0.25, .5, .75, 1.0, 1.5, 2.0, 2.5}. For any fixed k, we choose 2.5 × 10 3 qubit states uniformly in the Bloch ball.…”