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Indian Journal of Pure & Applied Physics

Assisted cloning of an arbitrary unknown two-qubit state via a genuine four-qubit entangled state and positive operator-valued measure

Lian Fang Han, Hao Yuan, Yang Ming, Zhuo‐Liang Cao

Published Aug 1, 2014• 3 citations
OpenAlex

Abstract

A protocol for cloning an arbitrary unknown two-qubit state and its orthogonal complement state with the assistance of a state preparer is presented. In this paper, a genuine four-particle entangled state which cannot be reduced to the product of two Bell states is used as the quantum channel. Moreover, positive operator-valued measure (POVM) instead of usual projective measurement is employed. In one hand, the usual teleportation is required. And in another hand, the perfect copies and complement copies of an unknown two-particle state can be implemented with a certain probability in the help of the state preparer.

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Communications in Theoretical Physics•May 1, 2013•2 citations
A protocol for cloning an arbitrary unknown two-qubit state and its orthogonal complement state with the assistance of a state preparer is presented. In this paper, a genuine four-particle entangled state which cannot be reduced to the product of two Bell states is used as the quantum channel. Moreover, positive operator-valued measure (POVM) instead of usual projective measurement is employed. In one hand, the usual teleportation is required. And in another hand, the perfect copies and complement copies of an unknown two-particle state can be implemented with a certain probability in the help of the state preparer.
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.
Two deterministic schemes are proposed to realize the assisted clone of an unknown four-particle entangled cluster-type state. The schemes include two stages. The first stage requires teleportation via maximal entanglement as the quantum channel. In the second stages of the protocols, two novel sets of mutually orthogonal basis vectors are constructed. With the assistance of the preparer through a four-particle or two-step two-particle projective measurement under these bases, the perfect copy of an original state can be produced. Comparing with the previous protocols which produce the unknown state and its orthogonal complement state at the site of the sender, the proposed schemes generate the unknown state deterministically.
Abstract The purpose of this article is to further investigate the assisted cloning of a d-dimensional arbitrary unknown state by utilizing quantum teleportation (QT) and remote state preparation (RST) techniques. We first propose a scheme for cloning an arbitrary unknown single-qudit state with assistance from a state preparer. In this scheme, the maximally and non-maximally bipartite d-dimensional states are used as quantum channels, respectively. In the first stage of scheme requires usual QT and in the second stage, the state preparer disentangles the left over entangled states by introducing one auxiliary qudit and performing a generalized CNOT, a single-qudit positive operator-valued measurement (POVM) and a single-qudit projective measurement process and conveys some classical messages to different parties so that a copy is produced probabilistically with the unit fidelity.Then by replacing the maximally or non-maximally bipartite d-dimensional entangled channel with a sequence of maximally or non-maximally bipartite d-dimensional entangled states as quantum channel, we can extend the above scheme to the case of cloning a d-dimensional arbitrary unknown m-qudit state with the unit fidelity and a certain probability in the help of the state preparer. PACS numbers 03.67.Hk, 03.67.-a, 03.65.Bz
A scheme to create a perfect copy of a three-qubit state with assistance from two preparers is proposed.During the course agreed in the scheme,the sender wish to teleport an unknown three-qubit entangled state which from two preparers to a remote receiver,and then create a perfect copy of the unknown state at her place.The scheme includes two stages.The first stage of the scheme requires usual teleportation.In the second stage,to help the sender realize the quantum cloning,two preparers perform three-qubit projective measurements on their own qubits which is from the sender,then the sender can acquire a perfect copy of the unknown state.The superiority of our protocol is that the rate of success about getting the copy can reach 1.
By making use of d-dimensional Hadamard gates and d-dimensional controlled NOT gates, we first construct a five-qudit maximally entangled state, and then use it as the quantum channel to propose a new bidirectional scheme for cloning two different arbitrary unknown single-qudit simultaneously under the assistance from a state preparer and the control of a supervisor. This scheme consists of two stages: quantum teleportation and assisted cloning. To fulfil the purpose, the first stage of this scheme requires bidirectional controlled teleportation via our constructed five-qudit maximally entangled state as quantum channel, where two distant communicators can simultaneously exchange their unknown single-qudit states with unit fidelity and unit probability under the permission of the supervisor.In the second stage,the state preparer disentangles any remaining entangled states by introducing two auxiliary particles, implementing a unitary transformation and two single-particle projective measurements. Subsequently, they transmit a specific number of classical bits to two distinct communicators in order to generate two precise replicas of different unknown states. Subsequently, the above scheme is extended with a certain probability and unit fidelity by replacing the above d-dimensional quantum channel with a five-qudit non-maximally entangled state. Finally, we further analyze the expansion issues of our scheme from the perspectives of positive operator-valued measurement (POVM for short), general quantum channel and the number of state preparers and controllers, and point out that the scheme is secure.
We propose a tripartite scheme for probabilistically teleporting an arbitrary two-qubit state with a four-qubit cluster-class state and a Bell-class state as the quantum channels. In the scheme, the sender and the controller make Bell-state measurements (BSMs) on their respective qubit pairs. With their measurement results, the receiver can reconstruct the original state probabilistically by introducing two auxiliary particles and making appropriate unitary operations and positive operator-valued measure (POVM) instead of usual projective measurement. Moreover, the total success probability and classical communication cost of the present protocol are also worked out.