量子隐形传态

Teleporting an unknown quantum state with unit

fidelity and unit probability via a non-maximally

entangled channel and an auxiliary system

Taghi Rashvand1,2

Received:5April2016/Accepted:21July2016/Published online:9August2016

©Springer Science+Business Media New York2016

Abstract We present a new scheme for quantum teleportation that one can teleport an unknown state via a non-maximally entangled channel with certainly,using an auxiliary system.In this scheme depending on the state of the auxiliary system,one canfind a class of orthogonal vectors set as a basis which by performing von Neumann measurement in each element of this class Alice can teleport an unknown state with unitfidelity and unit probability.A comparison of our scheme with some previous schemes is given and we will see that our scheme has advantages that the others do not.

Keywords Quantum teleportation·Non-maximally entangled channel

1Introduction

The transmission of information is one of the interesting processes of quantum infor-mation.Quantum teleportation is a process of transmission of information,a state of a system,from one place to another.For thefirst time in1993,Bennett et al.designed a scheme for teleportation[1].They used a system in a maximally entangled state as a quantum channel.In their scheme,Alice performs a Bell state measurement on her two systems,the system in an unknown state and one half of the maximally entangled system,and then sends her result to Bob who applies a local unitary operation to recover the unknown state.In this scheme,standard scheme,the existence of maximal entanglement is necessary.If one has a non-maximally entangled system,one has to B Taghi Rashvand

Taghi.rashvand88@

1Faculty of Science,University of Imam Khomeini International,Qazvin,Iran

2Tajhizsazanpishro Co.,Qazvin,Iran

4840T.Rashvand first convert the non-maximally entangled system to the maximally entangled system and then follow the standard scheme.Actually,in order to get fewer maximally entan-gled systems,it is necessary to provide many non-maximally entangled systems and perform a purification procedure[2]on them.

In the standard scheme,the existence of a Bell state measurement and a maximally entangled system are necessary.In other words,Alice and Bob have to share the max-imally entangled system and she also has to perform the Bell state measurement if they want to teleport correctly and completely.One can ask a question:Is there any scheme in which the existence of the maximally entangled system and the Bell state measurement are not necessary?To answer this question,many attempts have been carried out[3–11].Agrawal and Pati have proposed a scheme that uses orthogonal vectors as a basis and teleports,in general,an unknown state with unitfidelity but not unit probability,i.e.,teleportation is possible only for two out of four possible mea-surement results[6].Some others have proposed schemes in which Alice and/or Bob must do additional tasks,say,Alice has to perform a POVM instead of von Neumann measurement[3,4,9,11],prepare an auxiliary system[11],Bob has to prepare an aux-iliary system[5],and theyfirst concentrate entanglement of the channel[2].Although these schemes have advantages,they have a big problem:They are probabilistic.In other words,if one uses the previous schemes which use a non-maximally entangled system as a quantum channel and a von Neumann measurement,one cannot teleport an arbitrary unknown state with both unitfidelity and unit probability.Thus,it is one of the important advantages of our scheme that one can teleport an unknown state with both unitfidelity and unit probability.

In this article,we try to answer this question.We provide a new scheme using an auxiliary system in a specific state and perform a measurement in a specific basis. Actually in our scheme,Alice and Bob share a non-maximally entangled system,and Alice performs the measurement on three systems,auxiliary system,system in an unknown state and her entangled system,and then sends her results to Bob.Finally, Bob applies a local unitary operator to receive the unknown state.

We should mention that there are experimental works reported on successful tele-portation[12–14].

2Deterministic teleportation

In this section,we present a novel scheme to teleport quantum information determin-istically.In other words,we want to show how Alice can teleport an unknown state with unitfidelity and unit probability using our scheme.To do so,she has to prepare an auxiliary system and make a von Neumann measurement in a proper basis,which spans a eight-dimensional Hilbert space,on her systems.

Let us assume Alice and Bob share a non-maximally entangled system which is in the state

|ψ 23=L(|0 2|0 3+l|1 2|1 3),|L|2=1

,(1)

1+|l|2

where l is a known complex number except zero.The subscripts2and3label Alice and Bob’s system,respectively.Assume system1which Alice wants to teleport to Bob