Journal of Quantum Information Science, 2013, 3, 1-5
http://dx.doi.org/10.4236/jqis.2013.31001 Published Online March 2013 (http://www.scirp.org/journal/jqis)
Efficient Three-Party Quantum Secure Direct
Communication with EPR Pairs
Xunru Yin1,2, Wenping Ma1, Dongsu Shen1, Chaoyang Hao3
1State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, China
2School of Mathematics and Systems Science, Taishan University, Tai’an, China
3Shandong Taikai Electric Automation Co., Ltd., Tai’an, China
Received January 30, 2013; revised March 2, 2013; accepted March 10, 2013
ABSTRACT
In order to get rid of the drawback of information leakage which existed in Chong et al.’s protocol (Opt. Commun., 284,
2011, 515-518), an efficient three-party quantum secure direct communication (3P-QSDC) based on some ideas of
quantum dense coding with EPR pairs is proposed, in which each entangled pair can be used to exchange a longer
length of secret message between three legal users. By improving the classical channels and the qubit transmissions, our
scheme can avoid this kind of drawback. Thus, the secret messages are not leaked out to other people from the public
information. Moreover, compared with Chong et al.’s protocol, our protocol can achieve higher efficiency.
Keywords: Quantum Secure Direct Communication; Quantum Dense Coding; Protocol Efficiency
1. Introduction
Quantum secure direct communication (QSDC) is an im-
portant branch of quantum cryptography, in which the
secret messages are directly transmitted in a quantum chan-
nel between two legitimate parties, say Alice and Bob,
without creating a private key to encode and decode the
messages. Since QSDC has a great advantage of uncon-
ditional security based on quantum mechanics for the
legal users to communicate, much attention has been fo-
cused on this research field and many schemes have been
presented [1-12].
In 2002, Long and Liu [1] proposed the first QSDC
scheme based on EPR pairs. Beige et al. [2] presented a
QSDC protocol based on the exchange of single photons.
Boström et al. [3] proposed a ping-pong QSDC scheme
based on EPR pairs, which was improved by Li et al. [4]
in 2011. Deng et al. [5] proposed an efficient QSDC
scheme. However, the mode of message transmission in
QSDC is one-way. Thus, in 2004, quantum dialogue or the
so-called bidirectional QSDC was proposed [7]. Recently,
many three-party QSDC schemes were proposed, in which
a party can obtain the other two parties’ messages simul-
taneously through a quantum channel. Jin et al. [10] pre-
sented a 3P-QSDC by using the GHZ states, and Man et al.
[11] improved this scheme. Chamoli [12] also presented a
3P-QSDC with GHZ states. In 2007, Wang et al. [13]
presented a 3P-QSDC by using EPR pairs. In 2011, Chong
et al. [14] proposed an enhancement on Wang et al.’
scheme [13]. They pointed out that the communication can
be paralleled and thus the protocol efficiency is improved.
For simplicity, References [13,14] are shortened as CH
protocol and WY protocol, respectively. From CH pro-
tocol, we can see that the main features of their work are
the paralleled communication and the improved protocol
efficiency. However, there are some questions in Chong
et al.’s scheme, which can be summarized as follows:
1) The qubit transmissions in WY protocol are thought
to be sequential by Chong et al., i.e., Alice → Bob →
Charlie → Alice. That is, every party needs to wait for
the other’s response. So in CH scheme, the qubit trans-
missions are designed as Alice → (Bob and Charlie) and
(Bob and Charlie) → Alice. However, the improvement
has the following disadvantages: (a) The goal here is to
save the response time throughout the process, but this
new way can lead to double workload in Alice’s site.
Thus, this improvement would be of no great importance
or value in practical application; (b) As will be described
later, the qubit transmission mode of CH protocol can
reduce 3P-QSDC protocol efficiency.
2) Chong et al. proposed an enhancement on Wang et
al.’s scheme, but this work only compared with Men et
al.’s scheme [11] in the qubit efficiency. However, Men
et al.’s scheme is based on GHZ states, while Chong et
al.’ is based on EPR states. So it is more forceful if they
can compare 3P-QSDC efficiency of their own scheme
with that of Wang et al.’s scheme.
3) From step 11 in CH protocol, we can see that there
exists a message correlation between three parties. Let us
C
opyright © 2013 SciRes. JQIS

X. R. YIN ET AL.
2
take for example. If
1n0, 0XY

, then
ABC
M
MM. Thus, from the public classical chan-
nels, Eve can know the secret bits transmitted by three
parties must be one of randomly, which
contains
 
,0,1, 1, 1

0,0
 
2 1
2 bit of information. This
insecurity is called information leakage or classical cor-
relation [15,16]. In fact, WY protocol also has this kind
of drawback.
212log1
In this paper, we present an efficient 3P-QSDC scheme
based on some ideas in quantum dense coding with EPR
pairs. Each photon pair can be used to exchange a long-
er length of secret message and the drawback of in-
formation leakage does not exist in our scheme. Moreover,
in an ideal quantum channel, the efficiency of CH protocol
is 50%, but our 3P-QSDC efficiency can be increased to
60%. Finally, the security of our scheme is analyzed.
2. Description of the Protocol
Firstly, let us introduce two-qubit entangled states. An
EPR pair is one of the four Bell states, i.e.,

11
00 11
22

 (1)

11
00 11
22

 (2)

11
01 10
22

 (3)

11
01 10
22

 (4)
where 0 and 1 are the up and down eigenstates of
Pauli operator
z

.

01 2  and

01 2  are the up and down eigenstates of
Pauli operator
x

. Let 01 and be four
local unitary operations. That is
2
,,UUU 3 U
000 11,UI  (5)
101 10, x
U    (6)
201 10 y
Ui    , (7)
300 11 z
U   . (8)
Suppose that Alice, Bob, and Charlie have a secret
message to exchange respectively. Their messages can be
assumed as the following in sequence:








  
  
112 2
1122
112 2
,,,,,, ,
,, ,,,,,
,,,,, ,
AN
BN
CN
Mijij ij
Mklklkl
Mpqpq pq


,
N
N
N
where .

,,,, ,0,1
nnnn nn
ijklpq
Three parties agree that the four Pauli operations rep-
resent two-bit classical information, respectively, i.e.,
0123
00, 01,10, 11UUUU

. (9)
An EPR pair can be transformed into another EPR pair
by performing the unitary operation .
Then the encoding of our 3P-QSDC can be summarized
as Table 1.

0,1, 2, 3
i
Ui
Now, let us describe the present protocol in detail by
the following steps.
Step 1. Alice prepares EPR pairs and each EPR
pair is one of the four Bell states randomly. Alice takes
one particle from each EPR pair to form two single pho-
ton sequences h
Q and t, where denotes the
first (the second) particle in each pair. She encodes her
message into t by performing the operation
N
Q

ht
Q


30,1, 2,Ui
i according to Equation (9). Alice pre-
pares five sets of decoy photons, 112
,,,
B
BCA
DDDD and
2A, randomly chosen from D0,1,, and

.
Moreover, she generates single photon sequence r, in
which the particles is defined a one-to-one correspon-
dence with the initial states prepared by herself, i.e.,
Q
0,1,
 


 , and


 .
Then Alice randomly inserts all particles in 1
B
D and
1A into h to form . She randomly inserts all
particles in 22
D Qa
h
Q
,,
B
C
DD A Da
t
Q
and r into to form
. Finally, Alice sends to Bob.
Q
a
t
Q
a
t
Q
Step 2. After Bob receives t, Alice announces the
positions of 22
Q
,,,
B
CA
DDDQ
r
and the states of 2
B
D.
Then Bob measures the particles in 2
B
D by using basis
z

or
x

. He can judge if the quantum channel is se-
cure by analyzing the error rate. If no, Bob aborts the
communication. Otherwise, after picking out t, he en-
codes his message into t by performing the operation
Q
Q


3Q 0,1, 2,
i according to Equation (9). After that,
Bob asks Alice to send him .
Ui a
ha
Q Step 3. After Bob receives h, Alice announces the
positions of 11
,
B
A
DD and the states of 1
B
D. Then Bob
measures 1
B
D and checks the quantum channel by ana-
lyzing the error rate. If the error rate exceeds the thresh
Table 1. Encoding of the present protocol.
initial state operation final state




0
I
U
1
I
U
2
I
U
3
I
U
0
I
U
1
I
U
2
I
U
3
I
U













X. R. YIN ET AL. 3
old, this protocol is aborted. Otherwise, Bob picks out
h and performs Bell measurements on h and t
(encoded sequence), which forms two new sequences
QQ Q
h
Q and . Let be
t
Q
  
12
,, ,0,1,2,3
BNi
Rrrrr

Bob’s measurement results, where 0, 1, 2, 3 denote
,, ,

  
respectively. Bob asks Alice to
announce the measurement basis of , then he meas-
ures r with the same basis to form . Subsequently,
Bob randomly inserts the particles in 1A into h
r
Q
r
Q
D
QQ

to
form , and randomly inserts the particles in
2and r into to form Q. Finally, he sends
to Charlie.
b
h
Q
A
,
C
DD
b
t
QQt
Qb
t
Step 4. After Charlie receives t, Bob announces the
positions of and the states of C. Then
Charlie measures C and checks the quantum channel
by analyzing the error rate. If the error rate exceeds the
threshold, this protocol is aborted. Otherwise, Charlie
encodes his message into t by performing the unitary
operations according to Equation (9). After picking out
r, Charlie measures this sequence with the basis an-
nounced by Alice. Next, Charlie randomly inserts the
particles in 2A into (encoded sequence) to form
. Then Charlie sends to Alice.
b
Q
2
,,
CA r
DD Q 
D
Dt Q
Q
D
Q
c
t
Q
c
t
Q
Step 5. After Alice receives , Charlie announces
the positions and the states of 2A. Alice measures
2A and verifies if the transmission of is secure by
analyzing the error rate. If no, the protocol is aborted.
Otherwise, Alice picks out t
c
Qt
D
Dc
t
Q
Q

which has been encoded
by herself, Bob, and Charlie. Finally, Alice asks Bob to
send her .
b
h
Q
Step 6. After Alice receives h, Bob announces the
positions and the states of 1A. Then Alice checks the
quantum channel by measuring 1A. If the transmission
of is insecure, the protocol is aborted. Otherwise,
after picking out 1A, Alice performs Bell measurement
on h and t
Q (encoded sequence), and she records
the measurement results as . Alice encodes 00,
01,10,11 into
b
Q
DD
A
R
b
h
Q
Q
D

,, ,

 
 
 respectively, thus
she can generate a corresponding bit string
according to the initial states
prepared randomly by herself in Step 1, where
.
  
11
,,, ,
NN
y xy

,0,1
Rx
11
xy
Step 7. Bob announces
B
R.
Step 8. Alice can obtain
B
M
and C
M
from and
A
R
B
R. Then Alice announces BC
M
MM R.
According to all above steps, Bob and Charlie can get
the other two users’ messages. Thus three parties can
exchange their secret messages successfully. The simple
steps can be seen in Figure 1. Decoding rules can be
described as: 1) According to Table 1, Alice can know
the final states in her site, which are also the initial states
in Bob’s site, from the initial states prepared by herself
and her own operations in Step 1. Combining the final-
Figure 1. Qubit transmissions.
states in Bob’ site


B
R, Alice can deduce Bob’s opera-
tions. Thus she obtains
B
M
. From the initial states


B
R and the final states


A
R in Charlie’s site, Alice
deduces Charlie’s operations. Thus she gets C
M
; 2) Bob
can deduce the final states in Alice’s site from his opera-
tions and
B
R
Q
, thus he can know Alice’s operations from
the initial states prepared by Alice (the measurement
result of r). Then Bob gets A
M
. Bob can know
from the measurement result of r
Q and obtains
R
CB
M
MMR

; 3) From the measurement result of
r
Q

, which is equal to that of , Charlie can know .
Then he obtains
r
Q R
B
C
M
MRM

 . From , Charlie
gets the initial states prepared by Alice. By
R
B
M
and
B, Charlie can deduce the initial states in Bob’s site,
which are also the final states in Alice’s site. Thus Char-
lie gets
R
A
M
.
3. Security Analysis
Now, we analyze the security of our protocol in detail
below. The transmission security of the particle sequences
in the present 3P-QSDC scheme is similar to that of
Chong et al.’s scheme which is based on security of
Wang et al.’s scheme. In addition, we can see that the
entangled photon pairs act as a quantum channel based
on the idea of two-step transmission in our protocol. If
the sequence is securely transmitted, Eve can not
obtain any encoded information because one can not gain
the secret messages from one particle of an EPR pair. On
the other hand, although contains a sub-sequence
r which directly corresponds to the initial states pre-
pared by Alice, Eve can not get any useful information
about Alice’s message or Bob’s. This is because the de-
coy photons in
a
t
Q
a
t
Q
Q
2
B
D are used for detecting the existence

X. R. YIN ET AL.
4
of eavesdroppers, and the communication will be aborted
by Alice and Bob if the eavesdropping checks fail. In the
same way, Eve can not obtain Charlie’s message through
Steps 4 and 5.
In our protocol, Eve can see the public information
B
R and
M
in the classical channels. Eve wants to get
some secret messages from
B
R and
M
. Next, we first
consider
B
R. We take for example and suppose
that
1N
B
R denotes

. From Table 1, Eve can infer the
final state in Alice’s site and Bob’s operation must be
one of









03 1
,, ,,,,,UU UU 
 
2
.
However, the initial states prepared by Alice in Step 1
are randomly
generated. Thus, if Eve guesses

3
,U 


(similar for
the other three cases), the initial states and Alice’s opera-
tions must be one of








 03 1
,, ,,,,,UUUU 

 2
. So there
are totally sixteen possibilities, which contains
 
2
16116log1164  bits for Eve. On the other
hand,
B
R contains nothing about C
M
, Eve can only
explore 4 bits of secret information exchanged between
Alice and Bob (each user has 2 bits). Thus Eve cannot
get any information from
B
R. Next, Eve may get a
message correlation between three parties by combining
with
M
. However, because has the nature of ran-
domness, Eve also cannot get any secret information. So
all the secret bits exchanged between three parties are not
leaked out from the classical channels.
R
4. Discussion and Conclusion
In the following, let us discuss the efficiency of the pre-
sent protocol. The efficiency of a quantum communica-
tion scheme is defined as

s
tt
bqb   [17], where
s
b
b
denotes the expected number of secret bits received
by the users, t is the number of transmitted qubits, and
t is the number of needed classical bits. In CH protocol,
we can see that
q

34 2NNN  , thus the efficiency
is 50%. In our scheme, 3P-QSDC protocol can achieve
higher efficiency with

67360%NNN  . For
clarity, we make a comparison between CH protocol and
our protocol, which can be seen in Table 2.
In this paper, we point out that CH protocol has a
drawback of information leakage and propose a new
Table 2. Comparisons of two protocols.
CH protocol Our protocol
Quantum resource
Message length
3P-QSDC efficiency
Information leakage
EPR pair
N
50%
Yes
EPR pair
2N
60%
No
protocol to get rid of this kind of drawback. Moreover,
our scheme has higher efficiency. In summary, our pro-
tocol is efficient and secure in theory.
5. Acknowledgements
This work was supported by the National Science Foun-
dation of China under grant No. 61072140; the 111 Pro-
ject under grant No. B08038; and the Specialized Re-
search Fund for the Doctoral Program of Higher Educa-
tion under grant No. 20100203110003.
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