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Journal of Zhejiang Normal University

Controlled teleportation of a three-particle partly entangled state by non-maximally entangled particles

Guo Fangxia

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The conventional approaches to controll quantum teleportation were based on maximally entangled quantum states.However,most of quantum states in reality were non-maximal entangled states due to environmental coupling in the preparation and transmission.A new method to controll quantum teleportation was presented by non-maximally entangled quantum channel.In the proposed approach,a non-maximally entangled 5-particle state was utilized as the quantum channel,one of the particles was selected as the controlling particle.The sender Alice makes Bell states measurement once and Hadamard measurements twice,and the controller Charlie performes an Hadamard measurement,so the receiver could get the quantum state which Alice wanted to send by performing appropriate unitary transformations determined by the sender and controller′s measurement results transmitted via classical channel.The scheme was a controlled quantum teleportation based on non-maximally entangled state with certain probabilisity and could be applied to remote quantum computation,quantum telecloning and quantum remote control.

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The conventional approaches to controll quantum teleportation were based on maximally entangled quantum states.However,most of quantum states in reality were non-maximal entangled states due to environmental coupling in the preparation and transmission.A new method to controll quantum teleportation was presented by non-maximally entangled quantum channel.In the proposed approach,a non-maximally entangled 5-particle state was utilized as the quantum channel,one of the particles was selected as the controlling particle.The sender Alice makes Bell states measurement once and Hadamard measurements twice,and the controller Charlie performes an Hadamard measurement,so the receiver could get the quantum state which Alice wanted to send by performing appropriate unitary transformations determined by the sender and controller′s measurement results transmitted via classical channel.The scheme was a controlled quantum teleportation based on non-maximally entangled state with certain probabilisity and could be applied to remote quantum computation,quantum telecloning and quantum remote control.
Most of quantum states in reality are non-maximal entangled states due to environmental coupling in preparation and transmission.A controlled method is presented for N-particle partly entangled state teleportation using non-maximally entangled quantum channel.In the proposed approach,a non-maximally entangled(N+2)-particle state is utilized as the quantum channel,one of the particles is selected as the controlling particle.The sender makes Bell states measurement once,Hadamard operations and |0〉 |1〉states measurements for N-1 times,and the controller performs a Hadamard measurement,whereafter the receiver makes appropriate unitary transformations and necessary projection measurements based on the sender's and controller's measurement results,then the controlled teleportation of N-particle unknown quantum state is achieved.The method is a controlled quantum teleportation scheme based on non-maximally entangled state with certain odds and the success probability is 2|a|2.
A bidirectional quantum controlled teleportation scheme using the entanglement property of six-qubit maximally entangled state was presented.In the theoretical scheme,the sixqubit maximally entangled state was employed as the quantum channel linking three legitimate participants.Users were both sender and receiver.Alice transmitted an arbitrary single qubit state of qubit ato Bob and Bob transmitted an arbitrary single qubit state of qubit bto Alice via the control of the supervisor Charlie.Users carried out the Bell state measurements on their own particles and publicly announced their measurement results via a classical channel.Then they operated proper unitary transformation on their own particles,respectively.The bidirectional quantum controlled teleportation was successfully realized.
We have explicitly shown a teleportation scheme which allows Alice to probabilistically teleport an unknown 2-particle entangled state to either of the two receivers,Bob or Charlie,by using a non-maximally entangled 5-particle state as quantum channel.The scheme can be generalized to teleport an unknown N-(particle) entangled state to M receivers using a(N·M+1)-particle state as quantum channel at the expense of performing one CNOT operation,N·M Hadamard operations,appropriate unitary transformation without performing Bell-state measurement.
It is shown that a maximally seven-qubit state can be utilized for perfect teleportation of arbitrary three qubit systems and controlled teleportation of an arbitrary three qubit state. For perfect teleportation, the sender first performs a Von-Neumann measurement on her qubits, then the sender(Alice) tells the measurement result to the receiver(Bob) via a classical channel, the receiver can reconstruct the original state by performing appropriate unitary transformations on his qubits at hand. For controlled teleportation, the sender firstly carries out proper Bell-state measurements and the controller(charlie) needs to operate a single-qubit measurement, the receiver can reconstruct the original state by applying appropriate unitary transformations on his qubits after he knows the measurement results of both the sender and controller. Besides, the two teleportation schemes can be realized with the maximal probability.
In this scheme, N pairs of non-maximally entangled particle are used as quantum channel to teleport an unknown N-particle entangled W state via entanglement swapping, which has more generality. In order to realize this teleportation, the sender Alice performs Bell-measurements on particles belonging to her. Then the sender sends the results to the receiver Bob through the classical channel. According to the results, Bob performs a corresponding unitary on particles to reconstruct the original state. And then, teleporting an unknown three-particle entangled W state is presented.
In this paper a new scheme for teleporting an unknown entangled state of two particles is proposed. To weaken the requirement for the quantum channel, without loss of generality, two communicators only share a non-maximally entangled two-particle state. Teleportation can be probabilistically realized if sender performs Bell-state measurements and Hadamard transformation and receiver introduces two auxiliary particles, operates C -not operation, single-qubit measurements and appropriate unitary transformations. The probability of successful teleportation is determined by the smaller one among the coefficients' absolute values of the quantum channel.