量子多对象旅行投票方案：匿名与安全的网络投票技术
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本文主要探讨了一种基于量子力学的多目标量子旅行投票方案（Multi-object Quantum Traveling Ballot Scheme）。该创新性方法旨在通过量子机制实现匿名且保密的投票过程，特别适用于候选人数众多的场景，例如网络投票等。在传统的投票方式中，通常面临信息安全性、隐私保护等问题，而量子技术的应用为解决这些问题提供了新的途径。
在量子遍历（QuantumTraversal）的概念下，这个投票系统利用了量子纠缠（Quantum Entanglement）这一特性。量子纠缠是量子信息科学中的基本现象，两个或多个粒子之间的量子态相互关联，即使相隔遥远，对其中一个粒子的操作也能瞬间影响到其他粒子的状态。这种非局域性质使得量子通信和计算得以超越经典方法的局限。
在本研究中，作者设计了一个投票系统，每个选民可以通过搜索大量数据库来投给自己心仪的候选人，而无需担心投票记录与身份被关联。这种设计确保了选民的匿名性，因为他们的投票行为不会直接暴露身份，同时投票过程也保持了秘密，防止被第三方窃取或篡改。
为了验证该方案的有效性和安全性，文章还进行了深入的理论分析和安全评估。研究者关注了以下几个关键领域：
1. **投票过程的量子化**：通过量子技术实现数据的加密和传输，确保投票信息在传输过程中不被截获或篡改。
2. **匿名性和保密性**：量子纠缠的使用有助于保护选民的个人信息，如投票选择和投票时间，防止被第三方追踪或识别。
3. **数据库搜索的效率**：量子搜索算法（如Grover's Algorithm）可能提高在海量数据中查找特定候选人的速度，降低了选举的时间复杂度。
4. **抵抗攻击的能力**：对系统进行安全性分析，包括对量子不可克隆定理的应用，以防止诸如“投票伪造”或“恶意投票”之类的攻击。
5. **适用范围**：由于能够处理大量候选人，该方案特别适合在网络投票等大规模、复杂投票环境中应用。
这篇论文提出了一种利用量子力学原理改进传统投票机制的方法，强调了量子纠缠和量子遍历在增强投票系统安全性方面的潜力。这不仅扩展了信息处理的边界，也为未来的投票系统设计提供了一种新颖且安全的解决方案。
152 CHINESE OPTICS LETTERS / Vol. 7, No. 2 / February 10, 2009
Multi-object quantum traveling ballot scheme
Yuan Li (
ooo
)
∗
and Guihua Zeng (
QQQ
BBB
uuu
)
Laboratory of Coding and Communication Security, Department of Electronic Engineering,
Shanghai Jiao Tong University, Shanghai 200240
∗
E-mail: yuanli@sjtu.edu.cn
Received April 3, 2008
Based on quantum mechanics, a traveling ballot scheme with anonymity and secrecy is introduced to realize
voting. By searching th e objects in large amount of data bases, every voter may cast votes to his desired
candidates. Therefore, the proposed scheme may be applied to voting with a great deal of candidates, such
as network voting and so on. The security analysis of the present scheme is also performed.
OCIS codes: 060.0060, 260.0260, 270.0270.
doi: 10.3788/COL20090702.0152.
Quantum mechanics provides novel features to infor-
mation processing, extending the capabilities beyond
those classical applications only. As a resource in qua n-
tum communication, quantum entanglement is valu-
able for accomplishing many quantum computation
and other applications
[1,2]
. The most prominent re-
searches are investigated in some fields such as quantum
computation
[3,4]
, quantum teleportation
[5,6]
, and quan-
tum cryptography
[7]
, with the latter being the most ma-
ture experimentally. Based on the creation of a multipar-
tite entangled state in quantum computation, the quan-
tum gate tha t lies beyond the capabilities of linear optics,
can be implemented practically
[8]
. Recently, bec ause the
Heisenberg spin systems are natural candidates for simu-
lating the interactions between qubits, the entanglement
in Heisenberg spin chain has been studed.
Motivated by these development in quantum entangle-
ment, we investigate its application in quantum voting
with the relation between entanglement and quantum
phase transition. In some situations, ballot protocol is
always effective that peo ple want to vote their desired
objects among a great deal of candidates such as the elec-
tronic balloting or to select more prevalent books in net-
work. Reliable voting pr otocol should hence be a private,
secure, and verifiable scheme
[9,10]
. In quantum informa-
tion, the security and anonymity in quantum ballot pro-
tocol are based on the quantum mechanics. It requires
that the voters need quantum resources for a remote state
preparation to r e alize their votes and the resources can
be applied into practice such as network voting with the
development of quantum network
[11]
. Generally, two au-
thorities are addressed, one is called agent who prepares
ballot states and the other is called tallyman who counts
the votes. To the vote, ea ch party has to make a choice
between yes or no. After a ll votes have been made, the
vote tally can be determined by a c ollective measurement
of tallyman and read directly from the computatio n basis
states.
In this letter, we describe a system of quantum anony-
mous traveling voting protocol. One authority prepa res
an entangled state for the secrecy of ballots. After get-
ting the list of all candidates from the agent, voters first
search their desired objects if there exist a great deal of
ones to choose. Every voter may cast votes to his suit-
able objects which are mayb e more than o ne. Resorting
to the quantum search algorithm
[4]
, voters may find them
quickly.
In the voting scheme, assume there are K voters
V
1
, ··· , V
K
, N ballot objects B
0
, ··· , B
N−1
, and two au-
thorities, i.e., an a gent and a tallyman. In the anony-
mous traveling ballot scheme, the main idea is that the
voters cast their votes orderly with a traveling state. L e t
N
2
-dimension space H = H
V
⊗ H
T
be Hilbert space,
where H
V
and H
T
are N -dimension subspaces. Assume
{|0i, ··· , |N − 1i} is a set of computational orthonormal
basis s tates, i.e., hi|ji = δ
ij
, i, j ∈ {0, 1 , ··· , N − 1}. In
space H, the agent firstly prepares an entangled system
pair (p
v
, p
t
) which is expressed as
|Ai =
1
√
N
(
N−1
X
n=0
|n, N − n − 1i) = U |Ai
V
⊗ |Ai
T
, (1)
where p
v
∈ H
V
, p
t
∈ H
T
, |n, N − n − 1i = |ni
V
⊗ |N −
n − 1i
T
, and U is an entanglement generatio n op e rator.
Furthermore, subscript V is voting site and T is author-
ity site. The agent then sends p
v
to the first voter V
1
.
Having re c e ived the system sent from the agent, if V
1
does not cast any one of these candida tes , he sends p
v
to the next voter. Otherwise, V
1
will research his de-
sired candidate for casting vote. Let τ be the suitable
candidate whom he wants to vote. In terms of gener-
alized Grover algorithm
[3,4]
, |Ai
V
may be expressed as
|Ai
V
= sin φ|αi + cos φ|βi, where φ = arcsin(
1
√
N
), and
|αi = |τi, |βi =
1
√
N
X
n6=τ
|ni. (2)
Employing a sea rching operator Q on the s tate |Ai
V
for
times o f r = round(
π
2
√
N), V
1
may obtain the desired
state |τi with the possibility near to 1. For ascertaining
whether the found element is state |τi, V
1
may resort to
an ancilla state |qi in a register R
(1)
which is held by him-
self. With a Boolean function g(x) : {0, ··· , N − 1} →
{0, 1}, extremely V
1
can obtain his desired sta te. As fol-
lowing, he will cast his vote to the candidate τ. Denote an
phase shifting op e rator acted by V
k
as M
(k)
n
= exp(iθ
n
),
where 1 < k < K, 0 < n < N, θ
n
= 2nπ/N. The state
|τi after V
1
casting his vote becomes
|V
1
i = M
(1)
τ
|τi = exp(iθ
τ
)|τi. (3)
1671-7694/2009/020152-04
c
2009 Chinese Optics Letters
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