International Journal of Quantum Information

In search of a way to securely transfer information, the scientific world uses entanglement with several qubits. However, the experimental feasibility of implementing communication protocols remains unclear. In this work, we indicate a one-to-one correspondence between a quantum dialogue and the quantum Stackelberg duopoly game. If we consider a controller-dependent communication protocol to be a sequential quantum game, the two players, Alice and Bob, can be compared to two firms, $A$ and $B$. Moreover, the controller Charlie can be assumed to be the arbiter. First mover advantage is a significant feature of the Stackelberg duopoly game, which is explained and proved in the protocol. Further, we propose a controller-independent bidirectional quantum dialogue using four-qubit maximally entangled states. The efficiency of the protocol is determined to be 50%.

Hermitian dual-containing codes are an important class of linear codes which have important applications in the construction of quantum codes. In this paper, two classes of Hermitian dual-containing almost MDS codes over finite fields are studied. By employing the Hermitian construction, a class of quantum codes with minimum distance $3$ and a class of quantum codes with minimum distance $4$ are constructed.

Most prior semi-quantum key distribution (SQKD) protocols are designed in the context of qubits. In this paper, we proposed an SQKD protocol using ($d$+1) quantum states in two mutually unbiased bases in the context of qudits without invoking the classical party’s measurement capability. It not only decreases the quantum states sent by quantum party by half, but also improves the efficiency of key rate than qubits do. To prove the security of present protocol, we first illustrate that the present protocol is completely robust, and then prove its unconditional security from information theoretical perspective by computing its key rate and noise tolerance against cloning-based individual attack. The unconditional security proof demonstrates that the higher dimension of quantum system is, the higher key rate can be obtained and the higher noise tolerance is allowed in depolarization channel.

The possibility of encoding classical string of information into a quantum string via CNOT operation and Hadamard gate is discussed. It has been shown that maximizing/minimizing the quantum correlation of the generated quantum string depends on the values of the initial classical strings. The kernel of each string, as well as, the total string had been examined, where by applying the Hadamard gate on the classical string, one can decrease its similarity as well as the similarity of the total kernel. However, in the absence of the Hadamard gate, the large similarity of the final quantum string has been observed. The kernel of the final quantum string may be used as an indictor of the security degree of the encoded information, where the large degree of security has depicted at small kernel. The high degree of security can be implemented by applying the Hadamard gate on only one classical string.

In this paper, we propose a method through which $n$-qubit states can simultaneously be bi-directionally transmitted between two users. We assume that Alice and Bob, the legitimate users, each have a $n$-qubit GHZ-like state and want to teleport it to the other party. Also, a four-qubit cluster state plays the role of the quantum channel of this bi-directional quantum teleportation. The protocol is based on the method that at first, each user, through a series of $\text{CNOT}$ gates, converts the $n$-qubit state into a single qubit and some $0$ qubits. Then, by means of the Bell state measurement and proper operation, the single qubit state is transferred over the channel between the two sides. By re-applying the $\text{CNOT}$ gates on the transmitted qubits and auxiliary $0$ states, each user reconstructs the initial GHZ-like state. Finally, we investigate the effects of some kind of noises on the density matrix of the channel due to its interaction with the environment and present a method to protect the channel against the bit-flip error.