Quantum Inf Process (2015) 14:1469–1486
Robust quantum dialogue based on the entanglement
swapping between any two logical Bell states and the
shared auxiliary logical Bell state
Received: 9 October 2014 / Accepted: 22 January 2015 / Published online: 11 February 2015
© Springer Science+Business Media New York 2015
Abstract In this paper, using the quantum entanglement swapping technologies under
the collective-dephasing noise and the collective-rotation noise, two robust quantum
dialogue protocols are proposed, respectively. The logical Bell states are used as the
traveling states to combat the collective noise. The auxiliary logical Bell state is shared
privately between two participants through the manner of direct transmission ﬁrst.
After encoded with the receiver’s secret messages, it swaps entanglement with its
adjacent logical Bell state. In this way, the information leakage problem is avoided.
Moreover, Eve’s active attacks can be detected with the help of decoy photon tech-
nology. For decoding, the Bell state measurements rather than the four-qubit joint
measurements are needed.
Keywords Quantum dialogue (QD) · Entanglement swapping · Logical Bell state ·
Collective-dephasing noise · Collective-rotation noise · Information leakage
Quantum secure direct communication (QSDC) is one of the most remarkable appli-
cations of quantum cryptography. QSDC is able to transmit secret messages instan-
taneously. In other words, QSDC is capable of transmitting secret messages directly
from the sender to the receiver without establishing a raw key to encrypt them ﬁrst.
Long and Liu  proposed the state-encoded two-step QSDC protocol, which is always
regarded as the ﬁrst QSDC protocol. After that, several representative QSDC proto-
cols were constructed, such as the ping-pong protocol of Bostrom and Felbinger ,
the operation-encoded two-step protocol of Deng et al. , the quantum one-time
T.-Y. Ye (
College of Information and Electronic Engineering, Zhejiang Gongshang University,
Hangzhou 310018, People’s Republic of China