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Chinese Physics Letters

Teleportation of an Unknown Quantum State via Partly Entangled States

Feng Xun-Li, Gong Shang-Qing, Zhongyang Wang, Xu Zhi-Zhan

Published Oct 1, 2000• 1 citation
Publisher

Abstract

The teleportation of an unknown quantum state from one observer to another is of great importance in quantum information. In the standard teleportation scheme, a maximally entangled state is demanded. However, it is difficult to prepare such states in practice, and real entangled states are always partly entangled. We present a scheme to teleport an unknown quantum state using two partly entangled states. We show that the teleportation can be realized with a certain probability.

DOI
10.1088/0256-307x/17/10/001

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The teleportation of an unknown quantum state from one observer to another is of great importance in quantum information. In the standard teleportation scheme, a maximally entangled state is demanded. However, it is difficult to prepare such states in practice, and real entangled states are always partly entangled. We present a scheme to teleport an unknown quantum state using two partly entangled states. We show that the teleportation can be realized with a certain probability.
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.
In this paper, two schemes for teleporting an unknown three-particle three-level entangled state are proposed. In the first scheme, two partial three-particle three-level entangled states are used as the quantum channels, while in the second scheme, three two-particle three-level non-maximally entangled states are employed as quantum channels. It is shown that the teleportation can be successfully realized with certain probability, for both two schemes, if a receiver adopts some appropriate unitary transformations. It is shown also that the successful probabilities of these two schemes are different.
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.
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 new representation of an arbitrary and unknown N -particle state is presented at first. As an application, a scheme for teleporting an arbitrary and unknown N -particle state is proposed when N pairs of two-particle non-maximally entangled states are utilized as quantum channels. After Alice (sender) makes Bell-state measurement on her particles, Bob (recipient) introduces an auxiliary particle and carries out appropriate unitary transformation on his particle and the auxiliary particle depending on classical information from Alice. Then, von Neumann measurement that confirms whether the teleportation succeeds or not is performed by Bob on the auxiliary particle. In order to complete the teleportation, another N -1 times operations need to be performed which are similar to the above ones. It can be successfully realized with a certain probability which is determined by the product of the smaller coefficients of non-maximally entangled pairs. All possible unitary transformations are given in detail.