Graph states are special multipartite entangled states that have been proven useful in a variety of quantum information tasks. We address the issue of characterizing and quantifying the genuine multipartite entanglement of graph states up to eight qubits. The entanglement measures used are the geometric measure, the relative entropy of entanglement, and the logarithmic robustness, have been proved to be equal for the genuine entanglement of a graph state. We provide upper and lower bounds as well as an iterative algorithm to determine the genuine multipartite entanglement.
In this paper,two fault tolerant channel-encrypting quantum dialogue(QD)protocols against collective noise are presented.One is against collective-dephasing noise,while the other is against collective-rotation noise.The decoherent-free states,each of which is composed of two physical qubits,act as traveling states combating collective noise.Einstein-Podolsky-Rosen pairs,which play the role of private quantum key,are securely shared between two participants over a collective-noise channel in advance.Through encryption and decryption with private quantum key,the initial state of each traveling two-photon logical qubit is privately shared between two participants.Due to quantum encryption sharing of the initial state of each traveling logical qubit,the issue of information leakage is overcome.The private quantum key can be repeatedly used after rotation as long as the rotation angle is properly chosen,making quantum resource economized.As a result,their information-theoretical efficiency is nearly up to 66.7%.The proposed QD protocols only need single-photon measurements rather than two-photon joint measurements for quantum measurements.Security analysis shows that an eavesdropper cannot obtain anything useful about secret messages during the dialogue process without being discovered.Furthermore,the proposed QD protocols can be implemented with current techniques in experiment.
In this paper,two information leakage resistant quantum dialogue(QD)protocols over a collective-noise channel are proposed.Decoherence-free subspace(DFS)is used to erase the influence from two kinds of collective noise,i.e.,collective-dephasing noise and collective-rotation noise,where each logical qubit is composed of two physical qubits and free from noise.In each of the two proposed protocols,the secret messages are encoded on the initial logical qubits via two composite unitary operations.Moreover,the single-photon measurements rather than the Bell-state measurements or the more complicated measurements are needed for decoding,making the two proposed protocols easier to implement.The initial state of each logical qubit is privately shared between the two authenticated users through the direct transmission of its auxiliary counterpart.Consequently,the information leakage problem is avoided in the two proposed protocols.Moreover,the detailed security analysis also shows that Eve’s several famous active attacks can be effectively overcome,such as the Trojan horse attack,the intercept-resend attack,the measure-resend attack,the entangle-measure attack and the correlation-elicitation(CE)attack.
An N-qubit Greenberger–Horne–Zeilinger(GHZ) state has many applications in various quantum information tasks and can be realized in different experimental schemes. A GHZ diagonal state evolves to another GHZ diagonal state in independent parallel Pauli channels. We give the explicit expression of the resultant GHZ diagonal state in terms of the initial state and channel parameters. If the initial state is a pure N qubit GHZ state or a three-qubit GHZ diagonal state admits a condition, the full separability criterion of the Pauli noisy state is equivalent to positive partial transpose(PPT)criterion. Thus the fully separable condition follows.
