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Communications in Theoretical Physics

Unknown State Transmission Using GHZ States via Collective Noise Channel

Li Dong, Xiu Xiao-Ming, Gao Ya-Jun, Chi Feng

Published Aug 1, 2010• 5 citations
Publisher

Abstract

Two protocols for transmitting an unknown single-photon state and an unknown non-maximally entangled EPR state are presented by using the quantum channel of three-phonton GHZ (Greenberger–Horne–Zeilinger) state, which can be realized with unitary success probability when collective noise is taken into account. The protocols can also be generalized to transmit multi-photon state or to realize quantum communication in collective noise channel.

DOI
10.1088/0253-6102/54/2/13

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Two protocols for transmitting an unknown single-photon state and an unknown non-maximally entangled EPR state are presented by using the quantum channel of three-phonton GHZ (Greenberger–Horne–Zeilinger) state, which can be realized with unitary success probability when collective noise is taken into account. The protocols can also be generalized to transmit multi-photon state or to realize quantum communication in collective noise channel.
Recently, Dong et al. [Commun. Theor. Phys. 54 (2010) 269-272] proposed two protocols for transmitting unknown quantum states over the collective-dephasing noise channel using Greenberger-Horne-Zeilinger (GHZ) state. This work further extends Dong et al.'s protocols over an insecure channel, in which malicious users attempt to reveal useful information from the transmitted quantum states. Moreover, a secure unknown single-photon transmission protocol will be proposed for collective-rotation noise channel, over which Dong et al.'s work fails to show their non-straight forward constructions.
Two schemes, using respectively the single three-particle maximal Greenberger-Horne-Zeilinger (GHZ) state and the two Einstein-Podolsky-Rosen (EPR) states as quantum channels, for deterministic teleportation of arbitrary three-particle GHZ state are proposed. These schemes are also generalized into the case of teleportation of arbitrary n-particle GHZ state (n≥4). The fidelity of teleportation when the quantum channels are affected by noise is discussed. It is found that when using single three-particle GHZ state which is affected by noise as quantum channel, the fidelity of teleportation is only related to the entanglement of the channel. However, when using two EPR states which is affected by noise as quantum channels, the fidelity of teleportation is related to the entanglement of both the channels and the unknown state to be delivered. Compared with previous proposals, our schemes require a reduced number of entangled states as quantum channels to achieve the same task.
A protocol for probabilistic cloning of a class of three-qubit Greenberger-Horne-Zeilinger (GHZ) state and its orthogonal complement state by using three maximally two-qubit entangled states as the quantum channel is proposed.In this protocol,Bob(the state receiver) can receive the unknown state via usual teleportation process.With the assistance of Victor(the state preparer), Alice(the state sender) can produce the perfect copies and complement copies of an unknown state. A protocol for the teleportation is given by using non-maximally entangled states as quantum channel,and the clones and complement clones of unknown state also can be obtained by Alice with assistance offered by the state preparer.
A scheme for probabilistic controlled teleportation of a triplet W state using combined non-maximally entangled channel of two Einstein–Podolsky–Rosen (EPR) states and one Greenberger–Horne–Zeilinger (GHZ) state is proposed. In this scheme, an (m + 2 )-qubit GHZ state serves not only as the control parameter but also as the quantum channel. The m control qubits are shared by m supervisors. With the aid of local operations and individual measurements, including Bell-state measurement, Von Neumann measurement, and mutual classical communication etc., Bob can faithfully reconstruct the original state by performing relevant unitary transformations. The total probability of successful teleportation is only dependent on channel coefficients of EPR states and GHZ, independent of the number of supervisor m. This protocol can also be extended to probabilistic controlled teleportation of an arbitrary N-qubit state using combined non-maximally entangled channel of N – 1 EPR states and one (m + 2 )-qubit GHZ.