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arXiv:quant-ph/9906110 · Journal of Experimental and Theoretical Physics

Quantum teleportation of an Einstein-Podolsy-Rosen pair using an entangled three-particle state

В. Н. Горбачев, Andrew I. Trubilko

Published Nov 1, 2000• 78 citations
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Abstract

Quantum teleportation of an Einstein-Podolsky-Rosen pair using maximally entangled triplets to two receivers is studied. The projection basis for combined three-particle measurements, from the results of which the unknown state can be reconstructed, is found. The basis contains states where only two of the three particles are maximally entangled.

DOI
10.1134/1.1334979

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Quantum teleportation of an Einstein-Podolsky-Rosen pair using maximally entangled triplets to two receivers is studied. The projection basis for combined three-particle measurements, from the results of which the unknown state can be reconstructed, is found. The basis contains states where only two of the three particles are maximally entangled.
A scheme to teleport an unknown two qubit state from Alice (the sender) to Bob (the receiver) using two Einstein Podolsky Rosen (EPR) pairs is presented, each EPR pair being shared by both Alice and Bob. Firstly, Alice combines each of the two particles in the teleported state with an EPR particle and makes Bell state measurement on each combination. Then she transmits the outcomes of her measurements to Bob classically. According to Alice′s measurement results, Bob can perform appropriate unitary operations on his two EPR particles to retrieve the initial state.
A scheme for teleporting an unknown quantum state of many particles is proposed. The scheme operates essentially by prearranging the sharing of an Einstein-Podolsky-Rosen-correlated pair of particles every time. We show that after performing a series of Bell-state measurements and single-particle unitary transformations, the unknown state of many particles, which was destroyed at one place, can be reconstructed at another place. Our scheme is actually obtained by generalizing an earlier scheme of Bennett et al. [ Phys. Rev. Lett. 70 (1993) 1895 ; 76 (1996) 722 ] known as quantum teleportation to the multiparticle case.
An unknown quantum state \ensuremath{\Vert}\ensuremath{\varphi}〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do so the sender, ``Alice,'' and the receiver, ``Bob,'' must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state \ensuremath{\Vert}\ensuremath{\varphi}〉 which Alice destroyed.
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.
A scheme for teleporting an arbitrary and unknown three-particle state from a sender to either one of two receivers is proposed. The quantum channel is composed of a two-particle non-maximally entangled state and two three-particle non-maximally entangled W states. An arbitrary three-particle state can be perfectly teleported probabilistically if the sender performs three generalized Bell-state measurements and sends to the two receivers the classical result of these measurements and either one of the two receivers adopts an appropriate unitary transformation conditioned on the suitable measurement outcomes of the other receiver. All kinds of unitary transformations are given in detail.