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A kind of novel three-party quantum secure direct communication protocol is proposed with the correlation of two-particle entangled state. In this scheme the qubit transmission forms a closed loop and every one of the three participants is both a receiver and a sender of particle sequences in the bidirectional quantum channels. Each party implements the corresponding unitary operations according to its secret bit value over the quantum channels and then extracts the other two parties’ unitary operations by performing Bell measurements on the encoded particles. Thus they can obtain the secret information simultaneously. Finally, the security analysis shows that the present three-party scheme is a secure protocol.

Quantum key distribution (QKD) is based on quantum mechanics and has the unconditional security, in which all legitimate users can distribute a shared key beforehand to make secure communications. Different from QKD, quantum secure direct communication (QSDC), another important application of quantum cryptography, can allow the messages to be read out after qubit transmission and then exchange the secret information between all parties directly without distributing a shared secret key.

In 2002, Long et al. [

In this paper, we propose a novel three-party QSDC protocol by using the idea of quantum dense coding on the two-particle EPR pair. The three parties in our scheme are peer entities and they transmit the particle sequences each other synchronously in a closed loop of qubit transmission. One party can obtain the other two parties’ secret messages through performing the joint measurement on the encoded particles. The rest of our scheme is structured as follows. Section 2 describes the whole protocol in detail. Section 3 analyzes the security of this protocol. Finally, Section 4 gives a conclusion briefly.

The four Bell states can be written as

Suppose

Now, we suppose Alice, Bob, and Charlie as the three parties in our scheme. Let

where

If the encoded particle is the second qubit, the rule is the following

Initial state | Operation on particle 1 | Operation on particle 2 | Final state |
---|---|---|---|

Next, we describe this protocol in detail.

Step 1. Alice/Bob/Charlie prepares

Step 2. After confirming (Bob, Charlie)/(Charlie, Alice)/(Alice, Bob) has received the mixed sequences, Alice/Bob/Charlie publishes the positions and the measurement basis

Step 3. After picking out the decoy particles, Bob/Charlie/Alice performs the unitary operations on

Step 4. After confirming that Alice/Bob/Charlie has received the mixed two sequences, the other two parties announce the positions and the corresponding measurement basis of the decoy particles. Then they check the security of quantum channels by comparing the measurement results of the decoy particles. If the error rate does not meet the requirement, the three parties abort the protocol; otherwise, they continue it.

Step 5. Alice/Bob/Charlie first picks out the decoy particles. Now, each party has two encoded sequences and performs Bell measurement orderly on the corresponding photon pairs in this two sequences, for instance, Alice performs Bell measurement on the EPR pairs in

From the above steps, we can see the qubit transmission forms a closed loop and every party sends or receives particles simultaneously. For conciseness, we take

and

respectively. Bob performs

Now we analyze the security of our scheme. From the five steps, we can see that there must be a security check over quantum channels when one party sends a particle sequence to another party. On the other hand, the decoy particles are chosen from

Then the whole system is in the state

where

If Eve wants to avoid any error, the following conditions should be satisfied

According to the above equations, we can have

On the other hand, in the security check step, the measurement basis are chosen from

From the correlations of Bell states, the state

Then the whole quantum system is in the following state

Similarly, from the above formula and the correlations of

That is, regardless of what the legitimate users take the measurement basis, the eavesdropper Eve cannot extract any useful information of the secret messages by observing the ancillary particle. Then our scheme is secure according to the above analysis and discussion.

In this paper, we propose a three-party quantum secret direct communication protocol with the bidirectional qubit transmission. In the whole process, we can see that all the parties form a return qubit circuit and they are peer entities. The three parties can exchange their own secret messages by using Bell measurement and unitary operations over the quantum channels. This scheme has a novel characteristic for the quantum return circuit and the member equivalence. However, the security discussion is based on the condition of ideal quantum channels. We have not considered the actual physical environment. In the quantum channel, noise and loss cannot be ignored with the particle transmission because they reduce the efficiency of quantum communication and increase the risk of information leakage. With the existing technologies, it has become more difficult to study such quantum communication protocols. We hope this problem can be solved in future research.

This work was supported by the Shandong Provincial Natural Science Foundation (No. ZR2013FQ011), the Project of Shandong Province higher Educational Science and Technology Program (No. J13LN60), Technology Development Projects of Tai’an (No.20140629-2) and Project of Taishan University Doctoral Fund (Y-01-2014020).