Commun. Theor. Phys. 56 (2011) 664–668 Vol. 56, No. 4, October 15, 2011
Deterministic Quantum Key Distribution Using Gaussian-Modulated Squeezed States
∗
HE Guang-Qiang (
Û2
r
),
†
ZHU Jun (
Á
d
), and ZENG Gui-Hua (
Q
B
u
)
National Key Laboratory on Advanced Optical Communication Systems and Networks, Department of Electronic
Engineering, Shanghai Jiaotong University, Shanghai 200240, China
(Received April 21, 2009; revised manuscript r e c e ived May 31, 2009)
Abstract A continuous variable ping-pong scheme, which is utilized to generate deterministic private key, is proposed.
The proposed scheme is implemented physically by using Gaussian-modulated squ eezed states. The deterministic char-
acteristic, i.e., no basis reconciliation between two parties, leads a nearly two-time efficiency comparing to the standard
quantum key distribution schemes. Especially, the separate control mode does not n eed in the proposed scheme so that
it is simpler and more available than previous ping-pong schemes. The attacker may be detected easily through the
fidelity of the transmitted signal, and may not be successful in the beam splitter attack strategy.
PACS numbers: 03.67.Dd, 03.67.Hk
Key words: Gaussian-modulated squeezed state, quantum key distribution, deterministic private key
The quantum key distribution (QKD) scheme
[1−6]
pro-
vides a novel way of generation and distr ibution of secret
key. Its security is guaranteed by the law of quantum
mechanics.
[7−9]
The intrinsic basis reconciliation, which
is significant in guaranteeing the security, means that
the standard QKD is nondeterministic. Unfortunately,
the nondeterministic proper ty results in loss of many
qubits, consequently, the efficiency is very low. To im-
prove the efficiency, several deterministic QKD schemes
were proposed.
[10−15]
In these papers, scheme
[13]
provides
a more complete and perfect secure communication proto-
col, while scheme
[14]
gives a special case of it with N = 1.
These schemes are implemented in discrete variable, while
the final key is generated through a message-mode and the
security is guaranteed by separate control-mode. How-
ever, the separate control-mode in the previous ping-pong
schemes lea ds a higher communication complexity and a
more complicated experimental realization. In addition,
discrete var iable is not easy in generation as well as detec-
tion so that continuous va riable (CV) becomes a favored
candidate in the quantum cryptography.
[16−23]
In this letter, a c ontinuous variable ping-pong scheme,
which is implemented by using the Gaussian-modulated
squeezed states, is proposed. Since the propo sed scheme
does not need the basis reconciliation when the communi-
cators, i.e., Alice and Bob, exchange the key information,
its efficiency is nearly two times of the standard CV QKD
schemes. Particularly, the separate control-mo de, which is
necessary in the discrete variable (DV) ping-pong schemes,
can be omitted. This characteristic makes the proposed
scheme be feasible in experimental realization. In addi-
tion, the channel capacity is higher than that of the DV
ping-pong schemes. The sec urity analysis based on Shan-
non information theory shows clearly the security aga ins t
the beam splitter attack strategy. In a loss channel, when
the transmission is larger than 0.728 the security is war-
ranted.
The proposed scheme, which is s ketched in Fig. 1,
executes the following. Step 1, Bob operates an initial
vacuum state |0i with either operator P = D(α)S(r) or
P
⊥
= D(iα)S(−r) which are regarded as a pair of bases,
where S(r) is the squeezing operato r and r is the sq uee z ed
factor, D(α) is a displacement operator which is employed
to add noise, and α is a real number. Step 2, Bob sends
the generated state to Alice through a public quantum
channel. Step 3, having operated the received state by a
proper displacement operator D(α
′
= x + ix), Alice re-
turns the state to Bob, where x is random number, which
is drawn from Gauss ian probability distribution. Step
4, if the base P is employed in the step 1, Bob applies
D(−α) on the returned mode, and measures X
1
. Oth-
erwise, Bob applies D(−iα) on the returned mode, and
measures X
2
. The canonical qua dratures X
1
and X
2
are
defined as X
1
= (
1
2
)(ˆa+ˆa
†
) and X
2
= (
1
2i
)(ˆa−ˆa
†
). Step 5,
Alice randomly selects some x values, and then sends the
chosen values and their corresponding time slo ts to Bob
through a public classic channel. Step 6, after has received
Alice’s va lues, Bob calculates statistica lly the fidelity by
using the received values and his corresponding measured
results. Then Bob detects whether Eve is a bsent or not
by using the calculated fidelity.
We explain briefly the protocol above in the physi-
cal way. Bob’s operation in step 1 yields a squeezed co-
herent state either |α, ri = D (α)S(r)|0i or |iα, −ri =
∗
Supported by the National Natural Science Foundation of China under Grant Nos. 61102053, 61170228, 60970109, and 60801051 and
Shanghai Jiaotong University Participate in Research Projects under Grant Nos. T030PRP18001 and T030PRP19035
†
E-mail: gqhe@sjtu.edu.cn
c
2011 Chinese Physical Society and IOP Publishing Ltd
http://www.iop.org/EJ/journal/ctp http://ctp.itp.ac.cn