Reliable quantum teleportation based on quantum dense coding

Journal of Optics Applications April 2013, Volume 2, Issue 3, PP.43-49

Reliable Quantum Teleportation Based on Quantum Dense Coding Haiming Long1, Zhiwen Zhao1, 2#, Xiaodong Xiong1, Qinting Han1, Yong Wang2 1. College of Information Science and Technology, Beijing Normal University, 19 Xinjiekou Outside Street, Beijing 100875, China 2. Key Lab of Inertial Technology for National Defense, Beihang University, 37 Xueyuan Road, Beijing 100191, China #Email:zhaozw126@126.com

Abstract The classical channel is required for the original quantum teleportation [1]. According to our analysis, the defect that the classical information is easily intercepted and substituted by some phony information poses a great threat to the reliability of quantum teleportation. In the paper, a scheme of reliable quantum teleportation is proposed, which utilizes the quantum dense coding to transmit the outcome of joint Bell basis measurement. Because our scheme can guarantee that the outcome of joint Bell basis measurement cannot be intercepted and substituted by the eavesdropper, the reliability of original quantum teleportation is guaranteed.

Keywords: Quantum Teleportation; EPR State; Quantum Dense Coding; Joint Bell Basis Measurement

1 INTRODUCTION Quantum entanglement refers to the nonlocal and nonclassical correlations among two or more quantum systems, or the mechanical properties of the association among the various subsystems or various degrees of freedom in a quantum system. This incredible feature with no classical counterpart is first discovered by Einstein, Podolsky and Rosen in their famous paper arguing the incompleteness of quantum mechanics. Quantum entanglement is one of the most striking features of quantum mechanics and considered to be the most important resource in various types of quantum information processing, such as quantum key distribution, quantum teleportation[1], quantum dense coding[2] and so on. These procedures without conventional counterpart cannot be realized by classical operations and communication without the help of entanglement.

Quantum teleportation, first proposed by Bennett el al.[1], as one of the important applications of quantum entanglement, is probably one of the most amazing quantum phenomena and a fundamental ingredient in quantum information processing. Different from classical communication, quantum teleportation provides a mechanism to reconstruct faithfully an arbitrary unknown one-particle state at a spatially distant location without the need of transferring any particle physically. During the process, a quantum channel involving the prior shared two-particle maximally entangled state and a classical channel to transfer additional classical information are required.

Since the pioneering proposition presented by Bennett et al.[1] in 1993, quantum teleportation has acquired considerable interest both on experimental and theoretical levels [3-15] due to its interesting applications in the rapidly evolving quantum information processing and the potential applications in future quantum communication networks as well as universal quantum computation. In the experimental field, the first proof-of-principle demonstrations were reported in Refs. [3, 4]. Afterwards, Zeilinger et al. [5] realized the high-fidelity teleportation of photons over a distance of 600 meters across the River Danube in Vienna, with the optimal efficiency that can be achieved using linearoptics.

Recently, Jian-Wei Pan et al. [6] reported free-space implementation of quantum teleportation over 16 km. In the theoretical field, Hong-Yi Dai et al. [7, 8] proposed a scheme to probabilistically teleport an unknown three-level đ?‘˜-particle entangled state and showed fewer entangled particles and lesser classical information than Bennett et al.’s original protocol [1]. Mark M. Wilde [9] focused on the analysis of the classical channel of quantum teleportation and - 43 www.joa-journal.org

developed a view that an optimal amount of classical noise benefits the fidelity of quantum teleportation.

Thus far, however, all the schemes of quantum teleportation of single qubit states rely on a classical channel to transfer additional classical information required to reconstruct the teleported states. Furthermore, Romano et al. [10] proved that the resources, i.e. a maximally entangled state and a one-way classical channel, are not only sufficient but also necessary for deterministically and faithfully sending quantum states through any fixed noisy channel of maximal rank, when a single use of the channel is admitted. Unfortunately, the classical information is very easy to be intercepted without being detected. Through our analysis, this defect poses a great threat to the reliability of quantum teleportation.

In this paper, a quantum teleportation scheme has been proposed, in which the quantum dense coding is utilized instead of the classical information to directly transmit the outcome of joint Bell basis measurement. Based on our analysis, the reliability of quantum teleportation can be guaranteed.

2 REVIEW ON QUANTUM TELEPORTATION AND QUANTUM DENSE CODING 2.1 Original Quantum Teleportation Let us give a brief introduction to the quantum teleportation presented by Bennett et al. [1] in 1993. Supposing that Alice wants to transmit the particle 1 |Ďˆâ&#x;Š1 = a|0â&#x;Š1 + b|1â&#x;Š1 to Bob, and the two-particle maximally entangled state that Alice and Bob share is |Ďˆâˆ’ â&#x;Š2,3 = 1⠄√2 (|0â&#x;Š2 |1â&#x;Š3 − |1â&#x;Š2 |0â&#x;Š3 ). Define quantum state |Ďˆâ&#x;Š1,2,3 as the joint state of particle 1 and the entangled state |Ďˆâˆ’ â&#x;Š2,3 : |Ďˆâ&#x;Š1,2,3 = |Ďˆâ&#x;Š1 ⊗ |Ďˆâˆ’ â&#x;Š2,3 . To achieve teleportation, Alice performs a joint Bell basis measurement on her particle1 and 2, then receives one of the four possible Bell states expressed as two classical bits s1 s2 where ∀đ?’ž ∈ {1,2}ďźŒsđ?’ž ∈ {0,1} and afterward transmits the outcome to Bob over a classical channel. Depending on the received two classical bits s1 s2 , Bob performs a corresponding unitary operation on his particle 3 of the shared entangled state. After this operation, the quantum state of particle1 which has been destroyed due to Alice’s joint Bell basis measurement, is reconstructed on particle 3 at Bob’s end. The state of Bob’s particle 3 is |Ďˆâ&#x;Š3 = a|0â&#x;Š3 + b|1â&#x;Š3 when teleportation is perfect.

2.2 Analysis of the Classical Information The key requirements of the original quantum teleportation are a quantum channel and a classical channel, in which the latter is to transfer two bits of classical information implying the outcome of joint Bell basis measurement.

However, it is pretty easy for the eavesdropper to intercept the classical information and transmit some phony information to Bob. Now we analyze the influence of the defect on the reliability of quantum teleportation. For the convenience of analysis, we consider the following two cases.

(A) The eavesdropper just intercepts the classical information.

(B) The eavesdropper intercepts the classical information and then transmits some phony information to Bob. For the case (A), it will not threaten the reliability of quantum teleportation and the eavesdropper cannot reconstruct the state of the particle 1. In the process of quantum teleportation, the particle 3 would be transmitted to Bob. In order to prevent the eavesdropper from interception, the decoy photons technique [16-18] can be used for eavesdropping detection. Through this way, the particle 3 would not be intercepted by the eavesdropper but received

by Bob. Consequently, even if the eavesdropper has successfully got the outcome of joint Bell basis measurement, he cannot reconstruct the state of the particle 1 and the process of quantum teleportation is unaffected.

For the case (B), it will pose a serious risk to the reliability of quantum teleportation. That is because after the joint Bell basis measurement on Alice’s particle 1 and 2, the state of Bob’s particle 3 will have been projected into one of −a the four states {(−b ), (−a ), (ba), (−b )} with the equal probability of 1/4. Only can the correct outcome of the joint Bell b a basis measurement reconstruct faithfully the state of the particle 1. Therefore, if the eavesdropper intercepts the classical information and then transmits some phony information to Bob, Bob will receive the phony information and consider them as Alice’s measurement outcome. Then Bob will perform an incorrect unitary operation on his particle 3. After this operation, the quantum state of particle1, which has been destroyed due to Alice’s joint Bell basis measurement, is not successfully reconstructed on particle 3 at Bob’s end, i.e. the state of Bob’s particle 3 is|Ďˆâ&#x;Š3 ≠- 44 www.joa-journal.org

a|0⟩3 + b|1⟩3 . Consequently, the reliability of quantum teleportation cannot be guaranteed.

However, some people might argue that a reliable encryption scheme can be found to transmit the classical information. Actually, all encryption techniques depend on the calculation complexity. Thus, with the development of computer technology especially quantum computer, the traditional cryptology will become insecure. That is to say, as long as the classical information is used to transfer the outcome of joint Bell basis measurement, the reliability of quantum teleportation cannot be guaranteed.

In this paper, our scheme can realize the reliable quantum teleportation, in which the quantum dense coding is utilized instead of the classical information to directly transmit the outcome of joint Bell basis measurement.

3 RELIABLE QUANTUM TELEPORTATION BASED on QUANTUM DENSE CODING In this section, a new way has been put forward to achieve reliable quantum teleportation, where two quantum channels involving two EPR pairs are utilized and the quantum channels don’t carry any classical information. It is assumed that Alice, the intended sender, wants to transmit the quantum state of an unknown particle 1 to Bob, the intended receiver, then we have |ψ⟩1 = a|01 ⟩ + b|11 ⟩, where |a|2 + |b|2 = 1.

(1) The two-particle maximally entangled states are |ψ− ⟩2,3 =

1 √2

and |ϕ+ ⟩4,5 =

1 √2

(|02 ⟩|13 ⟩ − |12 ⟩|03 ⟩),

(2)

(|04 ⟩|05 ⟩ + |14 ⟩|15 ⟩).

(3)

The quantum teleportation can be achieved with the following steps: Step 1: Alice and Bob share the two-particle maximally entangled state |ψ− ⟩2,3 and Alice and Bob receives the particle 2, particle 3, respectively. Define quantum state |ψ⟩1,2,3 as the joint state of particle 1 and the entangled state |ψ− ⟩2,3 : 1 (|02 ⟩|13 ⟩ − |12 ⟩|03 ⟩) |ψ⟩1,2,3 = |ψ⟩1 ⊗ |ψ− ⟩2,3 = (a|01 ⟩ + b|11 ⟩) ⊗ √2 a b = (|01 02 13 ⟩ − |01 12 03 ⟩) + (|11 02 13 ⟩ − |11 12 03 ⟩).

(4) √2

√2

Step 2: To achieve teleportation, Alice performs a joint Bell basis measurement on her particle1 and particle 2. It is need to note that the joint Bell basis measurement is the process of establishing entanglement between particle 1 and particle 2. The quantum system constituted by particle 1 and particle 2 can be expressed by the following Bell bases. |ψ± ⟩1,2 = |ϕ± ⟩1,2 =

1 √2 1 √2

(|01 12 ⟩ ± |11 02 ⟩),

(5.1)

(|01 02 ⟩ ± |11 12 ⟩),

(5.1)

Based on the four orthogonal bases above, the three-particle system can be expressed as 1 1 |ψ⟩1,2,3 = |ψ− ⟩1,2 (−a|03 ⟩ − b|13 ⟩) + |ψ+ ⟩1,2 (−a|03 ⟩ + b|13 ⟩) 2 2 1

1

2

2

+ |ϕ− ⟩1,2 (b|03 ⟩ + a|13 ⟩) + |ϕ+ ⟩1,2 (−b|03 ⟩ +a|13 ⟩),

(6)

It can also be expressed in vector form as 1

−a |ψ⟩1,2,3 = [|ψ− ⟩1,2 (−b ) + |ψ+ ⟩1,2 (−a ) + |ϕ− ⟩1,2 (ba) + |ϕ+ ⟩1,2 (−b ) ]. b a 2 3

3

3

3

(7)

Now, supposing that Alice performs a joint Bell basis measurement on her particle1 and particle 2, the four measurement outcomes, i.e.|ψ− ⟩1,2 , |ψ+ ⟩1,2 , |ϕ− ⟩1,2 and |ϕ+ ⟩1,2 , are equal, each occurring with probability 1/4. At the same time, the state of particle 3 held by Bob will have been projected into a new state, which must be directly related to the original state of particle 1 and in correspondence with the measurement outcome. The corresponding relationship between the state of particle 3 and the outcome of the joint Bell basis measurement can be represented as the following table 1.

- 45 www.joa-journal.org

TABLE 1 THE STATE OF PARTICLE 3 AFTER THE JOINT BELL BASIS MEASUREMENT AT ALICE’S END

The outcome of the joint Bell basis measurement |đ?œ“ − â&#x;Š1,2 |đ?œ“ + â&#x;Š1,2 |đ?œ™ − â&#x;Š1,2 |đ?œ™ + â&#x;Š1,2

The state of particle 3 −đ?‘Ž ( ) −đ?‘? −đ?‘Ž ( ) đ?‘? đ?‘? ( ) đ?‘Ž −đ?‘? ( ) đ?‘Ž

Consequently, as long as Alice transmits the outcome of the joint Bell basis measurement to Bob, Bob can make a corresponding unitary operation on particle 3 to recover the state of particle 1.

In the original scheme [1], Alice will express the outcome of the joint Bell basis measurement as two classical bits s1 s2 where ∀đ?’ž ∈ {1,2}ďźŒsđ?’ž ∈ {0,1} and then transmit them to Bob via a classical channel. But in our scheme, we utilize the quantum channel instead of the classical channel.

Step 3: Alice and Bob share the two-particle maximally entangled state|Ď•+ â&#x;Š4,5 and Alice and Bob receives the particle 4, and particle 5, respectively. In accordance with the outcome of the joint Bell basis measurement, Alice performs corresponding unitary operation containing {I, X, Z, Y} on particle 4. Before the operation, the rule agreed

by Alice and Bob is as follows: The outcomes of the joint Bell basis measurement |Ďˆâˆ’ â&#x;Š1,2 , |Ďˆ+ â&#x;Š1,2 , |Ď•âˆ’ â&#x;Š1,2 and |Ď•+ â&#x;Š1,2 correspond to the unitary operation I, X, Z and Y respectively, so the transformation outcomes are as follows.

TABLE 2 THE TRANSFORMATION ON PARTICLE 4 AT ALICE’S END

The outcome of the joint Bell basis measurement

Corresponding to the transformation

|đ?œ“ − â&#x;Š1,2

đ?œ™0 = (đ??ź ⊗ đ??ź)|đ?œ™ + â&#x;Š4,5

|đ?œ“ + â&#x;Š1,2

đ?œ™1 = (đ?‘‹ ⊗ đ??ź)|đ?œ™ + â&#x;Š4,5

|đ?œ™ − â&#x;Š1,2

đ?œ™2 = (đ?‘? ⊗ đ??ź)|đ?œ™ + â&#x;Š4,5

|đ?œ™ + â&#x;Š1,2

đ?œ™3 = (đ?‘Œ ⊗ đ??ź)|đ?œ™ + â&#x;Š4,5

The state after transformation 1 (|04 â&#x;Š|05 â&#x;Š + |14 â&#x;Š|15 â&#x;Š) √2 1 (|04 â&#x;Š|15 â&#x;Š + |14 â&#x;Š|05 â&#x;Š) √2 1 (|04 â&#x;Š|05 â&#x;Š − |14 â&#x;Š|15 â&#x;Š) √2 1 (|04 â&#x;Š|15 â&#x;Š − |14 â&#x;Š|05 â&#x;Š) √2

Step 4: Alice transmits the transformed particle 4 to Bob, and then Bob performs Control-NOT transformation on the two entangled particles 4 and particle 5. The role of Control-NOT transformation is CNOT [ CNOT [

1 √2 1

√2

(|04 â&#x;Š|05 â&#x;Š Âą |14 â&#x;Š|15 â&#x;Š)] =

(|04 â&#x;Š|15 â&#x;Š Âą |14 â&#x;Š|05 â&#x;Š)] =

1 √2 1 √2

(|04 â&#x;Š|05 â&#x;Š Âą |14 â&#x;Š|05 â&#x;Š) =

(|04 â&#x;Š|15 â&#x;Š Âą |14 â&#x;Š|15 â&#x;Š) =

1

(|04 â&#x;Š Âą |14 â&#x;Š)|05 â&#x;Š,

(8.1)

(|04 â&#x;Š Âą |14 â&#x;Š)|15 â&#x;Š.

(8.2)

√2 1 √2

So we can get the states of the two entangled particles, and the outcomes are shown in table 3.

TABLE 3 THE MEASUREMENT OUTCOME OF OPERATING THE CONTROL-NOT GATE AT BOB’S END

Input State đ?œ™0 = đ?œ™1 = đ?œ™2 = đ?œ™3 =

1 √2 1 √2 1 √2 1 √2

(|04 â&#x;Š|05 â&#x;Š + |14 â&#x;Š|15 â&#x;Š) (|04 â&#x;Š|15 â&#x;Š + |14 â&#x;Š|05 â&#x;Š) (|04 â&#x;Š|05 â&#x;Š − |14 â&#x;Š|15 â&#x;Š) (|04 â&#x;Š|15 â&#x;Š − |14 â&#x;Š|05 â&#x;Š)

After the Control-NOT transformation 1 (|04 â&#x;Š|05 â&#x;Š + |14 â&#x;Š|05 â&#x;Š) √2 1 (|04 â&#x;Š|15 â&#x;Š + |14 â&#x;Š|15 â&#x;Š) √2 1 (|04 â&#x;Š|05 â&#x;Š − |14 â&#x;Š|05 â&#x;Š) √2 1 (|04 â&#x;Š|15 â&#x;Š − |14 â&#x;Š|15 â&#x;Š) √2

Particle 4 1 √2 1 √2 1 √2 1 √2

Particle 5

(|04 â&#x;Š + |14 â&#x;Š)

|05 â&#x;Š

(|04 â&#x;Š + |14 â&#x;Š)

|15 â&#x;Š

(|04 â&#x;Š − |14 â&#x;Š)

|05 â&#x;Š

(|04 â&#x;Š − |14 â&#x;Š)

|15 â&#x;Š

It can be seen from the table 3 above that Bob can measure particle 5 without the destruction of the quantum state of particle 4.

Step 5: Bob performs the Hadamard transformation on particle 4. The role of Hadamard transformation is as follows.

The expression of Hadamard gateďźˆreferred to H-gateis - 46 www.joa-journal.org

H= thus

1 √2

[(|0â&#x;Š + |1â&#x;Š)â&#x;¨0| + (|0â&#x;Š − |1â&#x;Š)â&#x;¨1|],

(9)

1 1 1 (|0â&#x;Š Âą |1â&#x;Š) H [ (|0â&#x;Š Âą |1â&#x;Š)] = { [(|0â&#x;Š + |1â&#x;Š)â&#x;¨0| + (|0â&#x;Š − |1â&#x;Š)â&#x;¨1|]} ∙ √2 √2 √2 1 1 = [(|0â&#x;Š + |1â&#x;Š)(â&#x;¨0|0â&#x;Š Âą â&#x;¨0|1â&#x;Š) + (|0â&#x;Š − |1â&#x;Š)(â&#x;¨1|0â&#x;Š Âą â&#x;¨1|1â&#x;Š)] = [(|0â&#x;Š + |1â&#x;Š) Âą (|0â&#x;Š − |1â&#x;Š)] 2 2 |0â&#x;Š

={ |1â&#x;Š

correspond to correspond to

1 √2 1 √2

(|0â&#x;Š + |1â&#x;Š) (|0â&#x;Š − |1â&#x;Š)

.

(10)

The outcomes of H-transformation on particle 4 performed by Bob are shown in the table 4 below.

TABLE 4THE OUTCOME OF OPERATING H-TRANSFORMATION ON PARTICLE 4 AT BOB’S END

Particle 4 1 √2 1 √2 1 √2 1 √2

The outcome of H-transformation

Particle 5

The state of Particle 4 and Particle 5

(|04 â&#x;Š + |14 â&#x;Š)

|04 â&#x;Š

|05 â&#x;Š

|04 05 â&#x;Š

(|04 â&#x;Š + |14 â&#x;Š)

|04 â&#x;Š

|15 â&#x;Š

|04 15 â&#x;Š

(|04 â&#x;Š − |14 â&#x;Š)

|14 â&#x;Š

|05 â&#x;Š

|14 05 â&#x;Š

(|04 â&#x;Š − |14 â&#x;Š)

|14 â&#x;Š

|15 â&#x;Š

|14 15 â&#x;Š

Note that the process of Step 4 and Step 5 is that Bob receives particle 4 and then performs a series of measurements on particle 4 and particle 5. According to the measurement outcome and the rule previously agreed with Alice, Bob can accurately get the outcome of the joint Bell basis measurement performed by Alice and the state of particle 3.

The correspondences are shown in the following table 5.

TABLE 5 THE CORRESPONDENCES OF A SERIES OF MEASUREMENT OUTCOMES

Bob’s measurement outcome

Alice’s unitary operation on particle 4

Alice’s Bell basis measurement outcome

|04 05 â&#x;Š

đ??ź

|đ?œ“ − â&#x;Š1,2

|04 15 â&#x;Š

đ?‘‹

|đ?œ“ + â&#x;Š1,2

|14 05 â&#x;Š

đ?‘?

|đ?œ™ − â&#x;Š1,2

|14 15 â&#x;Š

đ?‘Œ

|đ?œ™ + â&#x;Š1,2

The state of Bob’s particle 3 −đ?‘Ž ( ) −đ?‘? −đ?‘Ž ( ) đ?‘? đ?‘? ( ) đ?‘Ž −đ?‘? ( ) đ?‘Ž

So far, Alice has successfully transmitted the outcome of joint Bell basis measurement to Bob utilizing the quantum dense coding. Presently, Bob has known the state of his particle 3.

Step 6: Having received the outcome of the joint Bell basis measurement performed by Alice on particle1 and particle 2, Bob will perform a corresponding unitary operation on particle 3.

TABLE 6 THE OUTCOME OF OPERATING UNITARY TRANSFORMATION ON PARTICLE 3 AT BOB’S END

The outcome of the joint Bell basis measurement performed by Alice |đ?œ“ − â&#x;Š1,2 |đ?œ“ + â&#x;Š1,2 |đ?œ™ − â&#x;Š1,2 |đ?œ™ + â&#x;Š1,2

Particle 3 −đ?‘Ž ( ) −đ?‘? −đ?‘Ž ( ) đ?‘? đ?‘? ( ) đ?‘Ž −đ?‘? ( ) đ?‘Ž

Unitary Transformation matrix −1 0 ( ) 0 −1 −1 0 ( ) 0 1 0 1 ( ) 1 0 0 1 ( ) −1 0

After unitary operation, the quantum state of particle3 is - 47 www.joa-journal.org

The outcome of transformed Particle 3 −đ?‘Ž đ?‘Ž −1 0 ( )( ) = ( ) 0 −1 −đ?‘? đ?‘? đ?‘Ž −1 0 −đ?‘Ž ( )( ) = ( ) 0 1 đ?‘? đ?‘? đ?‘Ž 0 1 đ?‘? ( )( ) = ( ) 1 0 đ?‘Ž đ?‘? đ?‘Ž 0 1 −đ?‘? ( )( ) = ( ) −1 0 đ?‘Ž đ?‘?

|ψ⟩3 = a|03 ⟩ + b|13 ⟩, where |a|2 + |b|2 = 1.

(11)

After finishing these steps, the quantum state of particle1 which has been destroyed due to Alice’s joint Bell basis measurement is reconstructed on particle 3 at Bob’s end.

4 DISCUSSION Our scheme of quantum teleportation utilized the quantum dense coding instead of the classical information to directly transmit the outcome of joint Bell basis measurement. In this section, we will discuss whether the scheme can guarantee the reliability of original quantum teleportation [1].

First, in our scheme, the outcome of joint Bell basis measurement cannot be intercepted. That is because one of the features of the quantum dense coding is that even if the particle 4 is intercepted, the information of the particle 4 cannot be achieved by the eavesdropper. For example, it is supposed that the outcome of the joint Bell basis measurement is |ϕ+ ⟩1,2 , Alice performs unitary operation Y on particle 4 and thus the state of the entangled pairs after transformation is 1 (|04 ⟩|15 ⟩ − |14 ⟩|05 ⟩) |ϕ+ ⟩4,5 = √2 Now, even if the particle 4 is captured by the eavesdropper, the measurement outcome of particle 4 is 0 with the probability of 1/2 or 1 with the probability of 1/2. So the eavesdropper gets nothing. That is to say, the outcome of joint Bell-basis measurement performed by Alice cannot be intercepted.

Second, the decoy photons technique [16-18] can be applied to perform all transmissions of particle 3 and 4, by which, whether the eavesdropper transmits some phony particles can be effectively detected, as well, the particle 3 and 4 would not be substituted by the eavesdropper.

Consequently, the reliability of quantum teleportation can be ensured.

5 CONCLUSION In this paper, it has been analysed that the classical information used in original quantum teleportation [1] can significantly impact the reliability of quantum teleportation. In order to resolve the problem, a quantum teleportation scheme was proposed, in which the quantum dense coding was employed to transmit the outcome of joint Bell basis measurement, and only two quantum channels are used, so the outcome of joint Bell basis measurement performed

by Alice cannot be intercepted by an eavesdropper. Accordingly, the reliability of original quantum teleportation can be effectively guaranteed.

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AUTHORS 1Haiming

Long (1987- ), master degree

candidate, the major field is Quantum Communication.

2Zhiwen

Zhao (1966- ), PhD. Professor, the major field is

Information Security.

Email: zhaozw126@126.com

Email: dragon_hm@163.com

- 49 www.joa-journal.org