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Physical Review A

Hybrid economical telecloning of equatorial qubits and generation of multipartite entanglement

Xin-Wen Wang, Guojian Yang

Published Jun 17, 2009• 41 citations

Abstract

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.

DOI: 10.1103/physreva.79.062315

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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.

We propose a scheme to realize quantum cloning of an unknown M -qudit equatorial-like entangled state. The first stage of the protocol requires teleportation. After the teleportation is accomplished, the receiver can reestablish the original state. In the second stage of the protocol, with the assistance (through a single-particle projective measurement) of the preparer, the perfect copy of an original state can be produced at the site of the sender. Our scheme requires a single maximally entangled qudit pair as the quantum channel and three dits classical communication. The scheme is feasible at the expense of consuming local resources which include M −1 ancillary qudits introduced by the receiver and additional bi-qudit operations. Moreover, we construct a sort of unitary transformations which ensure ancillary qudits are not necessarily introduced by the sender. Comparing to the previous protocols, the proposed protocol is economical due to that the cost of both quantum nonlocal resources and classical communication is lowest.

Symmetric

N \to M

telecloning and remote quantum state inference

Teleporting unknown quantum states between distant nodes of a network is a significant feature of quantum communication. Few studies, however, have been conducted on

N \to M

telecloning, in which

N

copies of an unknown quantum state are optimally teleported to

M \geq N

receivers. Previous work requires global POVMs on all copies and auxiliaries; here, we show that symmetric

N \to M

telecloning can be probabilistically performed using only sequential (or parallel) Bell state measurements (BSMs), allowing the copies to be spatially separated. When successful, the fidelity of each receiver's reduced state saturates the bound imposed by the no-cloning theorem, with the probability of success being independent of

M

. In the case of an `unsuccessful' BSM, we show that the teleportation fidelity is likely to remain high, with the measurement outcome also providing information about the closest Pauli eigenbasis to the unknown state being telecloned. In this sense, each receiver can remotely infer the unknown quantum state with a level of confidence that scales with the number of copies, even if the fidelity of their own reduced state is sub-optimal. We additionally analyze the required resources to ensure the classical-communication fidelity bound is surpassed, both in terms of two-qubit inseparability and varying classes of multipartite entanglement. Surprisingly, we uncover that, at a given iteration of the protocol, pairwise entanglement is not always necessary to increase the teleportation fidelity and is never required to beat the classical bound for

N \geq 2

.

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.

We propose a generalization of quantum teleportation: the so-called many-to-many quantum communication of the information of a d-level system from N spatially separated senders to

M>N

receivers situated at different locations. We extend the concept of asymmetric telecloning from qubits to d-dimensional systems. We investigate the broadcasting of entanglement by using local $\stackrel{\ensuremath{\rightarrow}}{1}2$ optimal universal asymmetric Pauli machines and show that the maximal fidelities of the two final entangled states are obtained when symmetric machines are applied. Cloning of entanglement is studied using a nonlocal optimal universal asymmetric cloning machine and we show that the symmetric machine optimally copies the entanglement. The ``many-to-many'' teleportation scheme is applied in order to distribute entanglement shared between two observers to two pairs of spatially separated observers.

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.