Eve can eavesdrop on the information if the quantum channel is noisy [19], and this ping-
pong protocol can be attacked without eavesdropping [20]. Furthermore, the capacity of
ping-pong protocol can be improved [21] and entanglement swapping can be used to modify
this protocol against attacks without eavesdropping [22].
As we know, quantum cryptography can b e considered unconditionally secure in theory
because any effective eavesdropping would be discovered by the users, which is assured by
the fundamental principles in quantum mechanics. Consequently, the users have to sample a
certain number of photons or key bits to detect eavesdropping in most quantum cryptography
protocols. An efficient way to detect implies high security or economization of resource. In
this paper, we modify the strategy to detect eavesdropping in ping-pong protocol and it
follows that a better security app ears in contrast to the original one. In addition, this
scheme can be applied to quantum sharing of classical secret (or QSCS for short). The
structure of this paper is as follows: In Sec.II, we introduce the modified ping-p ong protocol,
and its security is discussed in Sec.III. Furthermore, this proto col can be generalized to QSCS
scheme (see Sec.IV), in which the above function of state |Ψ
±
i is used similarly. Finally, a
conclusion is given in Sec.V.
II. The modified ping-pong protocol
In this Section, we will present a modified ping-pong protocol which, as we will show, has
higher security than Bostr¨om and Felbinger’s one [14]. For simplicity, the original ping-pong
protocol will be represented as OPP, while our modified ping-pong protocol as MPP.
Let us discuss the strategy to detect eavesdropping in OPP first. To obtain security, as
narrated in the above section, both Alice and Bob perform a local measurement on their
qubits in the basis B
z
. Because the two qubits are in state |Ψ
+
i initially, they will draw a
conclusion that Eve does not exist when their results are opposite. Obviously, it does not
make full use of the state |Ψ
+
i. As we know, two qubits has a four-dimensional state space
and four Bell states ( |Ψ
±
i =
1
√
2
(|01i ± |10i), |Φ
±
i =
1
√
2
(|00i ± |11i)) construct a complete
orthogonal basis of this space. In fact, |Ψ
−
i and |Ψ
+
i have the same property, as far as this
kind of measurement is concerned. That is, both |Ψ
−
i and |Ψ
+
i yield opposite results with
certainty. Therefore, any state in the form |ψi = α|Ψ
+
i + β|Ψ
−
i (|α|
2
+ |β|
2
= 1) can pass
3
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