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arXiv:1402.1914 · Journal of Physics B Atomic Molecular and Optical Physics

Manipulation of tripartite-to-bipartite entanglement localization under quantum noises and its application to entanglement distribution

Xin-Wen Wang, Shi-Qing Tang, Ji-Bing Yuan, Le-Man Kuang

Published Dec 24, 2014• 1 citation
arXivHTMLPDF

Abstract

This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localization, and that the optimal strategy for reducing a three-qubit GHZ state to a two-qubit one via local measurements and classical communications in the amplitude-damping case is different from that in the noise-free case. We also show that the idea of entanglement localization could be utilized to improve the quality of bipartite entanglement distributing through amplitude-damping channels. These findings might shed a new light on entanglement manipulations and transformations.

DOI
10.1088/0953-4075/48/2/025502

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This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localization, and that the optimal strategy for reducing a three-qubit GHZ state to a two-qubit one via local measurements and classical communications in the amplitude-damping case is different from that in the noise-free case. We also show that the idea of entanglement localization could be utilized to improve the quality of bipartite entanglement distributing through amplitude-damping channels. These findings might shed a new light on entanglement manipulations and transformations.
The effect of quantum noise on entanglement localization is investigated. We show that the optimal strategy for reducing a multiparticle entangled state to a two-particle one via local measurements in the noise-free case is different from that in a noisy environment, and explore the best von Neumann measurement on one of three qubits of a triple Greenberger-Horne-Zeilinger state for extracting a two-qubit entangled state in the presence of local amplitude noises. We also demonstrate that the idea of entanglement localization can be utilized to improve the quality of bipartite entanglement distributing through noisy quantum channels. These results might shed a new light on entanglement manipulations and transformations.
The effects of distributing entanglement through the amplitude damping channel or the phase damping channel on the teleportation of a single-qubit state via the Greenberger–Horne–Zeilinger state and the W state are discussed. It is found that the average fidelity of teleportation depends on the type and rate of the damping in the channel. For the one-qubit affected case, the Greenberger–Horne–Zeilinger state is as robust as the W state, i.e., the same quantum information is preserved through teleportation. For the two-qubit affected case, the W state is more robust when the entanglement is distributed via the amplitude damping channel; if the entanglement is distributed via the phase damping channel, the W state is more robust when the noisy parameter is small while the Greenberger–Horne–Zeilinger state becomes more robust when it is large. For the three-qubit affected case, the Greenberger–Horne–Zeilinger state is more robust than the W state.
We systematically characterize quantum entanglement in all sixteen combinations of two-qubit Bell states across three operational regimes: pure superposition, noiseless mixing, and asymmetric mixing of one noisy and one pure Bell state. For pure superpositions, we calculate the von Neumann entropy and show that entanglement depends critically on the relative phase phi between superposed states. For mixed states, we use concurrence C under three physically motivated decoherence channels. The Depolarizing (DP) and Phase Damping (PD) channels are modeled as global, collective operations on the two-qubit Hilbert space, while Amplitude Damping (AD) is treated as independent local decay on each qubit, reflecting the asymmetric, energy-dissipating nature of spontaneous emission. A central and counterintuitive result is that increasing noise can raise concurrence in specific parameter regimes across all three channels. We further map the boundary between mathematical entanglement (C > 0) and operational quantum non-locality using the Horodecki criterion, finding this boundary to be strongly channel-dependent. Under Phase Damping, the Bell-local entanglement regime vanishes entirely for identical and same-bases mixtures, meaning any surviving entanglement guarantees a CHSH violation. Under Depolarizing noise, a large Bell-local region requires mixing probability r > 1/sqrt(2) to recover non-locality at maximum noise. For Amplitude Damping, certain mixtures exhibit a non-monotonic Horodecki parameter M(T): concurrence decreases monotonically with noise, yet the capacity for CHSH violation is lost at intermediate noise levels and restored at high noise, as maximal damping repurifies the noisy branch. These results provide a unified analytical reference for entanglement and non-locality management across Bell-state combinations and decoherence channels relevant to NISQ architectures.
Ardehali (Phys. Rev. A, 46, 5375 (1992). 10.1103/PhysRevA.46.5375 ) derived a Bell-type inequality for an n-particle system in a Greenberger–Horne–Zeilinger (GHZ) state. This inequality helps relax the detection efficiencies required for closing the detection loophole in Bell tests. Coffman et al. (Phys. Rev. A, 61, 052306 (2000). doi: 10.1103/PhysRevA.61.052306 ) gave a simplified form of tripartite entanglement of three-qubit pure states. We use theory and experiment to investigate both results using three-qubit GHZ states with different intensities of bit-flip noise. The purpose of our work is to relate the Ardehali inequality and the tripartite concurrence of the tripartite GHZ states in a noisy environment. Our results show that the experimental values are quite consistent with theoretical predictions for three-qubit GHZ states in a bit-flip noisy environment.
Abstract In this paper quantum teleportation of an unknown quantum state via noisy maximally bipartite (Bell) and maximally tripartite (Greenberger–Horne–Zeilinger (GHZ)) entangled states are investigated. We suppose that one of the observers who would receive the sent state accelerates uniformly with respect to the sender. The interactions of the quantum system with its environment during the teleportation process impose noises. These (unital and nonunital) noises are: phase damping, phase flip, amplitude damping and bit flip. In expressing the modes of the Dirac field used as qubits, in the accelerating frame, the so-called single mode approximation is not imposed. We calculate the fidelities of teleportation, and discuss their behaviors using suitable plots. The effects of noise, acceleration and going beyond the single mode approximation are discussed. Although the Bell states bring higher fidelities than GHZ states, the global behaviors of the two quantum systems with respect to some noise types, and therefore their fidelities, are different.
Quantum teleportation in the presence of noisy channels acting on a bipartite resource state is considered. We consider a family of generalized noisy channels that continuously connect the amplitude damping and the dephasing channels, encompassing a wide family of in-between scenarios, to delve into the relation between the teleportation success and the amount of three- and four-partite entanglement (distributed among the qubits of the resource state and those representing local environments) generated during the evolution. Our analysis reveals that for a fixed entanglement of the resource state, the channels that better protect the teleportation fidelity against the detrimental effects of noise are those that generate higher amounts of (Greenberger-Horne-Zeilinger--type) multipartite entanglement. This suggests that the dynamically induced multipartite correlations may serve as an additional resource for teleportation and provides insight into the characterization of processes and of the type of induced entanglement according to their ability to assist the protocol.