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Chinese Journal of Quantum Electronics

Assisted cloning of a class of unknown three-qubit GHZ state

Shi Shou-Hua

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
We proposed a protocol for probabilistic cloning of an unknown two-particle entangled state and orthogonal complement state based on three particle GHZ state.In this scheme,the state which Alice wants to cloning was completely unknown and arbitrary for Alice and Bob.First,Alice made Bell measurement on his particles and sended his measurement results to Bob via classical channel.After having received Alice's classical message,Bob could reconstruct the original state on her particles by unitary operation and control-not gate operation.Second,Alice could produce the perfect copies and complement copies of an unknown state with assistance of the state preparer.Our scheme also fit to the case that the quantum channel was non-maximally.Furthermore,the quantum entangled resource and the classical communication cost were greatly reduced compared with other protocol.
Our concern is to design an assisted-clone scheme which can produce a perfect copy of a three-particle Greenberger—Horne—Zeilinger (GHZ) class state with a high probability. In the first stage of the protocol, the sender teleports the input state to the receiver by using three EPR pairs as the quantum channel. In the second stage of the protocol, a novel set of mutually orthogonal basis vectors is constructed. With the assistance of the preparer through a three-particle projective measurement under this basis, the perfect copy of an original state can be reestablished by the sender with the probability 1/2. Moreover, the classical communication cost of the scheme is also calculated.
We propose a protocol where one can realize quantum cloning of an unknown two-particle entangled state and its orthogonal complement state with assistance offered by a state preparer. The first stage of the protocol requires usual teleportation using a (or two) four-particle entangled state(s) as quantum channel(s). In the second stage of the protocol, with the assistance (through a two-particle projective measurement) of the preparer, the perfect copies and complement copies of an unknown state can be produced.
Our concern is to design an assisted-clone scheme which can produce a perfect copy of a three-particle Greenberger-Horne-Zeilinger(GHZ)class state with a high probability.In the first stage of the protocol,the sender teleports the input state to the receiver by using three EPR pairs as the quantum channel.In the second stage of the protocol,a novel set of mutually orthogonal basis vectors is constructed.With the assistance of the preparer through a three-particle projective measurement under this basis,the perfect copy of an original state can be reestablished by the sender with the probability 1/2.Moreover,the classical communication cost of the scheme is also calculated.
In this paper, we proposed a protocol which can produce a perfect copy of an unknown three-particle three-dimension equatorial entangled state with assistance from a state preparer. Two stages were included in this protocol. The first stage requires usual teleportation, after Alice's (the state sender) generalized Bell-state measurement. Bob (the state receiver) can get the original state with a certain probability. In the second stage, after having received Victor's (the state preparer) classical message, and using the rest resource of the teleportation process, the perfect copy of an original unknown state can be produced in Alice's place. Furthermore, we have also investigated that the quantum channel is a non-maximally entangled state case. Alice also can re-establish the original unknown state in the certain probability.
We first propose a novel protocol to realize quantum cloning of an arbitrary unknown shared state with assistance offered by a state preparer. The initial phase of this protocol involves the utilization of quantum teleportation (QT), enabling the transfer of quantum information from an arbitrary number of senders to another arbitrary number of receivers through a maximally entangled GHZ-type state serving as a network channel, without centralizing the information at any specific location. In the second stage of this protocol, the state preparer performs a special single-qubit projective measurement and multiple Z-basis measurements and then communicates a number of classical bits corresponding to measurement results, the perfect copy or orthogonal-complementing copy of an unknown shared state can be produced at senders hands. Then, using a non-maximally entangled GHZ-type state instead of the aforementioned quantum channel, we extend the proposed protocol from three perspectives: projective measurement, positive operator-value measurement (POVM), and a single generalized Bell-state measurement. Our schemes can relay quantum information over a network without requiring fully trusted central or intermediate nodes, and none of participants can fully access the information.