Narrow Results

Adding the maximally mixed state with some weight to the entanglement system leads to disentanglement of the latter. For each predefined entangled state there exists a minimal value of this weight for which the system loses its entanglement properties. These values were proposed to be used as a quantitative measure of entanglement called robustness [G. Vidal and R. Tarrach, Phys. Rev. A 59, 141 (1999)]. Using the concurrence, we propose the derivation of this measure for the system of two-qubit. Namely, for a two-qubit pure state, an exact expression of robustness is obtained. Finally, in the same way, the robustness of special cases of mixed two-qubit states is calculated.

We investigated the geometric phase for interaction between superconducting two-qubit system in dephased environment. The Pancharatnam phase and the Berry phase are studied. Numerical results are discussed. By considering the differently initial conditions, we find that the time-dependent Pancharatnam phase keeps the initial entangling message. On the other hand, the transition of Pancharatnam phase is dependent of the phase change in the superconducting two-qubit coupling system. Our results may be helpful to implement the time-dependent geometric quantum computation.

We present a novel method to judge the entanglement of two-qubit system, the density matrix of a two-qubit system can be constituted by the principle density matrix ${\rho }_p$ and the separable density matrices ${\rho }_1$–${\rho }_4$. The necessary and sufficient conditions for the two-qubit system, the three involved coefficients p${}_p\ge$ 0, p${}_1\ge$ 0, p${}_2\ge$ 0, and the principal density matrix ${\rho }_p$ being separable, then the two-qubit system is separable, otherwise the two-qubit system is entangled. Finally, the criterion for several known density matrices have been verified in this way.