Quantum Teleportation of a Three-qubit State using a Four-qubit Entangled State

Abstract

Recently Liu et al.(Int. J. Theor. Phys. 53:4079, 2014) had shown that a special form of three-qubit entangled state can be teleported by using a five‐ qubit cluster state. However, we demonstrate that five-qubit cluster state and five-qubit von-Neumann projective measurements are not necessary to complete the protocol. The special three-qubit state can be teleported via a four-qubit entangled state, by introducing one ancillary qubit and one controlled-not operation. Physical realization of the proposed four-qubit entangled state and the generalization to teleport the multi-qubit state is also presented. Introduction Quantum teleportation is one of the most astonishing features of quantum mechanics. An unknown quantum state can be teleported from one site to another via previously shared entanglement assisted by classical communications and local operations. In 1993, Bennett et al. [1] proposed the first protocol of quantum teleportation of an arbitrary single-qubit state using a maximally entangled two-qubit state. Four years later, this protocol was experimentally demonstrated [2]. Thereafter, teleportation of an arbitrary single-qubit state was proposed using tripartite GHZ state [3], four-partite GHZ state [4], SLOCC equivalent W-class state [5], cluster state [6], etc. Teleportation of an arbitrary two-qubit state was proposed using tensor product of two Bell states [7], tensor product of two orthogonal states [8], genuinely entangled five-qubit state [9], five-qubit cluster state [10], six-qubit genuinely entangled state [11], etc. Recently, Liu et al. [12] had shown that a special form of three-qubit entangled state can be teleported by using a five-qubit cluster state based on five-qubit von-Neumann projective measurements and local unitary operations. However, we demonstrate that five-qubit cluster state and five-qubit von-Neumann projective measurements are not necessary to complete the protocol. The special three-qubit state can be teleported via a four-qubit entangled state, by introducing one ancillary qubit and one controlled-not (CNOT) operation. The proposed four-qubit entangled state can be physically realized by a pair of Bell states and two single-qubit states. The generalization of the protocol to teleport a multi-qubit state is also presented. Quantum Teleportation of a Three-qubit State In [12], a special form of three-qubit state is given by (1) where . Our teleportation scheme can be described as follows. Suppose Alice has an unknown three-qubit state . She wants to send this state to a distant receiver Bob. Alice and Bob share a four-qubit entangled state