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arXiv:1109.5335 · Chinese Physics Letters

One-to-Many Economical Phase-Covariant Cloning and Telecloning of Qudits

Xin-Wen Wang, Su Yu-Huan, Guojian Yang

Published Oct 1, 2010• 12 citations
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Abstract

We present explicit unitary transformations for realizing both symmetric and asymmetric one-to-many economical phase-covariant clonings of qudits. We also propose a corresponding telecloning scheme. It is shown that the fidelity of the telecloning with nonmaximally entangled states can be larger than that of the corresponding cloning. This implies that partially entangled states can be better than the maximally entangled states for our economical phase-covariant telecloning scheme.

DOI
10.1088/0256-307x/27/10/100303

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We present explicit unitary transformations for realizing both symmetric and asymmetric one-to-many economical phase-covariant clonings of qudits. We also propose a corresponding telecloning scheme. It is shown that the fidelity of the telecloning with nonmaximally entangled states can be larger than that of the corresponding cloning. This implies that partially entangled states can be better than the maximally entangled states for our economical phase-covariant telecloning scheme.
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We propose a simple scheme for hybrid economical telecloning (HETC) of equatorial qubits with the well-known W-type entangled states. The so-called HETC is a synthesis of several types of quantum cloning and quantum teleportation, in which economical symmetric and asymmetric clonings and anticlonings can be simultaneously achieved by teleportation. We use the global fidelity and average-single-qubit fidelity to estimate, respectively, the collective copying quality and show that the two criteria lead to different results. We obtain interesting equalities and inequalities about the fidelities of clones or anticlones. We also introduce controlled HETC of equatorial qubits with recently proposed Greenberger-Horne-Zeilinger (GHZ)--W-type entangled states [L. Chen and Y. X. Chen, Phys. Rev. A 74, 062310 (2006)], in which the achievement of phase-covariant telecloning between the sender (Alice) and the receivers (Bobs) is conditioned on the collaboration of all the supervisors (Charlies). This idea may open a perspective for the applications of such interesting type of entangled states. A method for generating the GHZ--W-type entangled states is also presented.
A scheme for implementing 1 → 2 symmetric economical phase-covariant telecloning of a bipartite entangled state is proposed based on a quantum logic network. The quantum circuits for preparing the telecloning channel and for teleporting the input state are presented, respectively. There is no ancilla needed for preparing the channel, and the fidelity of telecloning is enhanced. Due to only single- and two-qubit operations being used in the whole process, it can be easily implemented in experiment.