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Probabilistic Quantum Clone via GHZ States

Chuanwei Zhang, Chuan‐Feng Li, Ziyang Wang, Guang‐Can Guo

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

We propose a probabilistic quantum clone scheme using GHZ states, Bell basis measurement, single-qubit unitary operations and generalized measurement, all of which are within the reach of current technology. Compared to another possible scheme via Tele-CNOT gate (Gottesman and Chuang, Nature 420, 390 (1999)), the present scheme may be used in experiment to clone the states of one particle to those of two different particles with higher probability and less GHZ resources.

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We propose a probabilistic quantum clone scheme using GHZ states, Bell basis measurement, single-qubit unitary operations and generalized measurement, all of which are within the reach of current technology. Compared to another possible scheme via Tele-CNOT gate (Gottesman and Chuang, Nature 420, 390 (1999)), the present scheme may be used in experiment to clone the states of one particle to those of two different particles with higher probability and less GHZ resources.
We propose a probabilistic quantum cloning scheme using Greenberger-Horne-Zeilinger (GHZ) states, Bell-basis measurements, single-qubit unitary operations, and generalized measurements, all of which are within the reach of current technology. Compared to another possible scheme via Tele-controlled-NOT gate [D. Gottesman and I. L. Chuang, Nature (London) 402, 390 (1999)], the present scheme may be used in experiment to clone the states of one particle to those of two different particles with higher probability and less GHZ resources.
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.
Utilizing Hadamard gates and controlled not gates, maximally entangled states of four, five and six qubits are generated. Then, we propose respectively controlled and assisted cloning schemes of unknown two-, three- and four-qubit states via these constructed states as quantum channels. Each of the three schemes includes two stages: controlled teleportation and assisted cloning. The controlled teleportation stage of our schemes all require a single-qubit [Formula: see text]-basis measurement by controller, and need different GHZ-state measurements by senders of three schemes to complete the transmission process of their respective quantum states. In the assisted cloning stage of our schemes, after the state preparers of three schemes perform respectively appropriate GHZ-state measurements, at the senders’ locations, perfect replicas and orthogonal complementary copies of unknown states will be produced through appropriate local quantum operations. Compared with usual assisted cloning schemes, every suggested plan is extremely efficient in terms of quantum resources, as it only requires a small number of GHZ-state measurements, significantly decreasing the need for quantum operations and classical resources. Through discussion, we conclude that our schemes are safe and can be extended to assisted cloning of unknown multi-qubit GHZ-state with multiple controllers.
A scheme for teleporting an unknown three-particle GHZ state from a sender to either one of two receivers through a non-maximally three-particle entangled GHZ state as quantum channel is proposed.An unknown three-particle entangled state can be perfectly teleported probabilistically if the sender performs a generalized Bell-state measurement and the Hadamard operations while either one of two receivers introduces two additional particles,performs the controlled-not(C-not) operations and introduces an appropriate unitary transformation with the help of the other receiver's the Hadamard operation and simple measurement.The present scheme may be directly generalized to teleport an unknown k-particle GHZ state from a sender to either one of two receivers by using a partial entangled three-particle GHZ state as the quantum channel,introducing(k-1) additional qubits and performing(k-1) C-not operations.
We present a scheme for probabilistic teleportation via a non-maximally entangled GHZ state. Quantum teleportation will succeed with a certain probability if the sender makes a generalized Bell state measurement, the cooperator performs a generalized XXX basis measurement, and the receiver introduces an auxiliary particle, performs a collective unitary transformation and makes a measurement on the auxiliary particle. The success probability of the teleportation is given. We also obtain the maximum of the success probability of the teleportation.