Probabilistic teleportation of two - particle entangled state

In this report, two different probabilistic teleportations of a two-particle entangled state by pure entangled three-particle state are shown. Their successful probabilities are different. 03.65.Bz, 03.67.-a Typeset using REVTEX ∗E-mail: [email protected] †E-Mail: [email protected] 1 Quantum teleportation, proposed by Bennett et.al [1], is the process that transmits an unknown two-state particle, or a qubit from a sender (Alice) to a receiver (Bob) via a quantum channel with the help of some classical information. In their scheme, such a quantum channel is represented by a maximally entangled Bell state. Teleportation has been demonstrated with the polarization photon [2] and a single coherent mode of field [3] in optical experiment. Recently, Gorbacher et. al [4] considered the quantum teleportation of twoparticle entangled state by three-particle entanglement, in their proposal, a three-particle Greenberger-Horne-Zeilinger [5] (GHZ) state is used as the communication channel. The three-photon GHZ state has been realized experimentlly [6]. In the proposal of standard teleportation, a Bell state or a GHZ state is used to as quantum channel for faithful teleportation. If the entangled state used as quantum channel is not maximally entangled, the faithful teleportation is not possible. Although Mor and Horodecki [7] showed that a “ conclusive ” teleportation of an unknown two-state particle can be made possible with pure entangled state of two-particle, whether a perfect teleportation of two-particle entangled state having a finite probability of success is possible with pure entangled state of three particles or not is unknown. In this report, a pure entangled three-particle state is considered, which is used as quantum channel. We present two schemes, by which, the probabilistic teleportations of two-particle entangled state can be realized. The successful probabilities of these two schemes are different. The probability of one scheme is equal to the twice modulus of the smaller coefficient of the pure entangled three-particle state. Let a pure entangled three-particle state be in the following state |Φ〉 123 = α |000〉 123 + β |111〉 123 (1) where, α, β are reals, |α| > |β| . The two-particle entangled state which will be teleported is: |Ψ〉 45 = a |00〉 45 + b |11〉 45 (2) The particle 3 of the state |Φ〉 123 and particle pair (4, 5) belong to the sender Alice. The state of particle pair (4, 5) is unknown to Alice. Other two particles 1, 2 belong to receiver 2 Bob. In order to realize the teleportation, a Bell state measurement on particles 3 and 4 is made by Alice, which will project particles 1, 2 and 5 into the following state: