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arXiv:quant-ph/0001081 · Physical Review A

Probabilistic quantum cloning via Greenberger-Horne-Zeilinger states

Chuanwei Zhang, Chuan-Feng Li, Zi-Yang Wang, Guang-Can Guo

Published Sep 6, 2000• 38 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.62.042302

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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.
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 scheme to teleport an arbitrary unknown two-particle state by a non-maximally three-particle entangled Greenberger–Horne–Zeilinger (GHZ) state and a non-maximally two-particle entangled state from a sender to either one of two receivers. We probabilistically teleport the arbitrary unknown two-particle state by performing two Bell-state measurements on the sender's side, introducing two appropriate unitary transformations on the receiver's side conditioned on a Hadamard operation and a projection measurement on the other possible receiver's side.
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 study the 1→ N faithful telecloning of two linear-independent states of a one-qubit system. Based on the analysis of the probabilistic cloning machine, we construct a multiparticle entangled state, and present a telecloning scheme under local operations and classical communication (LOCC). The success probability is greater than half of the optimal probability of the probabilistic cloning machine. Specifically, we show how to prepare the three-particle entangled state needed by 1→2 telecloning under LOCC using the Greenberger-Horne-Zeilinger state as a resource. All the operations in 1→2 telecloning are within the reach of current technology.
We discuss the (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancilla under local operation and classical communication. Whereas any two orthogonal Greenberger-Horne-Zeilinger (GHZ) states taken from the canonical GHZ basis can be cloned with the help of a known GHZ state, surprisingly we find that no two WWW states can be cloned by using any known three qubit (possibly entangled) state as a blank copy.