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Journal of Physics B Atomic Molecular and Optical Physics

Controlled teleportation of continuous variables

Ding Nie, Guangqiang He, Guihua Zeng

Published Aug 26, 2008• 4 citations
Publisher

Abstract

A controlled quantum teleportation of continuous variable using a tripartite Greenberger–Horne–Zeilinger (GHZ) state is proposed. The protocol enables controlling the fidelity of bipartite teleportation by shifting the phase of one of the three modes involved in the teleportation. This method reduces the quality of the tripartite entanglement and by quadrature measurements of the changed mode, bipartite entanglement can be distilled from the original entanglement. Because of the phase shift, the quality of the bipartite entanglement is inferior to the entanglement distilled from the original GHZ-state. By controlling the quality of the entanglement we realize the controlled teleportation.

DOI
10.1088/0953-4075/41/17/175504

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A controlled quantum teleportation of continuous variable using a tripartite Greenberger–Horne–Zeilinger (GHZ) state is proposed. The protocol enables controlling the fidelity of bipartite teleportation by shifting the phase of one of the three modes involved in the teleportation. This method reduces the quality of the tripartite entanglement and by quadrature measurements of the changed mode, bipartite entanglement can be distilled from the original entanglement. Because of the phase shift, the quality of the bipartite entanglement is inferior to the entanglement distilled from the original GHZ-state. By controlling the quality of the entanglement we realize the controlled teleportation.
Quantum teleportation protocols of continuous variable (CV) Greeberger–Horne–Zeilinger (GHZ) and Einstein–Podolsky–Rosen (EPR) entangled states are proposed, and are generalized to teleportation of arbitrary multimode GHZ entangled states described by Van Loock and Braunstein (2000 Phys. Rev. Lett. 84 3482). Each mode of a multimode entangled state is teleported using a CV EPR entangled pair and classical communication. The analytical expression of fidelity for the multimode Gaussian states which evaluates the teleportation quality is presented. The analytical results show that the fidelity is a function of both the squeezing parameter r, which characterizes the multimode entangled state to be teleported, and the channel parameter p, which characterizes the EPR pairs shared by Alice and Bob. The fidelity increases with increasing p, but decreases with increasing r, i.e., it is more difficult to teleport the more perfect multimode entangled states. The entanglement degree of the teleported multimode entangled states increases with increasing both r and p. In addition, the fact is proved that our teleportation protocol of EPR entangled states using parallel EPR pairs as quantum channels is the best case of the protocol using four-mode entangled states (Adhikari et al 2008 Phys. Rev. A 77 012337).
The teleportation of a two-particle entangled state, using a Greenberger-Horne-Zeilinger triplet, for continuous variables is studied. The basis for joint three-particle measurements is found, where the vectors describe the states in which only two of three particles are entangled. It represents the measurement of the momentum of one particle and the difference of coordinates and the sum of momenta of the two other particles. An optical realization of this scheme is presented, which uses squeezed states of light and reduces the measurement of momentum and coordinate to the detection of quadrature operators of the electromagnetic field.
Controlled quantum teleportation is an important extension of multipartite quantum teleportation, which plays an indispensable role in building quantum networks. Compared with discrete variable counterparts, continuous variable controlled quantum teleportation can generate entanglement deterministically and exhibit higher superiority of the supervisor's authority. Here, we define a measure to quantify the control power in continuous variable controlled quantum teleportation via Greenberger-Horne-Zeilinger-type entangled coherent state channels. Our results show that control power in continuous variable controlled quantum teleportation increases with the mean photon number of coherent states. Its upper bound is 1/2, which exceeds the upper bound in discrete variable controlled quantum teleportation (1/3). The robustness of the protocol is analyzed with photon absorption. The results show that the improving ability of the control power will descend by the increasing photon loss, with the upper bound unchanged and robust. Our results illuminate the role of control power in multipartite continuous variable quantum information processing and provide a criterion for evaluating the quality of quantum communication networks.
A quantum teleportation network involving multiple users is essential for future quantum internet. So far, controlled quantum teleportation has been demonstrated in a three-user network. However, versatile and controlled quantum teleportation network involving more users is in demand, which satisfies different combinations of users for practical requirements. Here we propose a highly versatile and controlled teleportation network that can switch among various combinations of different users. We use a single continuous-variable six-partite Greenberger–Horne–Zeilinger (GHZ) state to realize such a task by choosing the different measurement and feedback operations. The controlled teleportation network, which includes one sub-network, two sub-networks and three sub-networks, can be realized for different application of user combinations. Furthermore, the coherent feedback control (CFC) can manipulate and improve the teleportation performance. Our approach is flexible and scalable, and would provide a versatile platform for demonstrations of complex quantum communication and quantum computing protocols.