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Optics and Spectroscopy

Robustness of multipartite entanglement under collisional decoherence

Yee‐Chia Yeo

Published Aug 1, 2007• 3 citations
Publisher

Abstract

The collision model of Ziman et al. was considered and the robustness of N -qubit Greenberger-Horne-Zeilinger (GHZ), W, and linear cluster states were studied. Our results show that N -qubit entanglement of GHZ states would be extremely fragile under collisional decoherence, and that of W states could be more robust than of linear cluster states.

DOI
10.1134/s0030400x07080127

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The collision model of Ziman et al. was considered and the robustness of N -qubit Greenberger-Horne-Zeilinger (GHZ), W, and linear cluster states were studied. Our results show that N -qubit entanglement of GHZ states would be extremely fragile under collisional decoherence, and that of W states could be more robust than of linear cluster states.
We consider the collision model of Ziman et al. and study the robustness of NNN-qubit Greenberger-Horne-Zeilinger (GHZ), WWW, and linear cluster states. Our results show that NNN-qubit entanglement of GHZ states would be extremely fragile under collisional decoherence, and that of WWW states could be more robust than that of linear cluster states. We indicate that the collision model of Ziman et al. could provide a physical mechanism for some known results in this area of investigation. More importantly, we show that it could give a clue as to how NNN-partite distillable entanglement would be relatively rare in our macroscopic classical world.
We study the robustness of multiparty entanglement under local decoherence, modeled by partially depolarizing channels acting independently on each subsystem. Surprisingly, we find that the robustness of (GHZ) entanglement increases with the number of qubits. An n-qubit Greenberger-Horne-Zeilinger (GHZ) state can stand more than 55% local depolarization in the limit $\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\infty}.$ GHZ states are more robust than other generic states of three and four qubits. We also study spin-squeezed states in the limit $\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\infty}$ and find that they too can stand considerable local depolarization.
We present a method to determine the decay of multiparticle quantum correlations as quantified by the geometric measure of entanglement under the influence of decoherence. With this, we compare the robustness of entanglement in Greenberger-Horne-Zeilinger (GHZ), cluster, WWW, and Dicke states of four qubits and show that the Dicke state is the most robust. Finally, we determine the geometric measure analytically for decaying GHZ and cluster states of an arbitrary number of qubits.
We investigate the robustness of multiparty nonlocality under local decoherence, acting independently and equally on each subsystem. To be specific, we consider an NNN-qubit Greenberger-Horne-Zeilinger (GHZ) state under a depolarization, dephasing, or dissipation channel, and examine nonlocality by testing violation of the Mermin-Klyshko inequality, which is one of Bell's inequalities for multiqubit systems. The results show that the robustness of nonlocality increases with the number of qubits, and that the nonlocality of an NNN-qubit GHZ state with even NNN is extremely persistent against dephasing.
We investigate the decay of entanglement, due to decoherence, of multiqubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness-optimization problem that only involves states equivalent, under local unitary transformations, to the Greenberger-Horne-Zeilinger ∣GHZ⟩|\text{GHZ}⟩∣GHZ⟩ state.