Based on some identities for the determinant of completely positive maps of rank two, concurrences are calculated or estimated from below.

We give “tight” and “loose” constructions suitable for specifying processes represented as sets of pomsets (partially ordered multisets). The tight construction is suitable for specifying “primitive” processes; it introduces the dual notions of concurrence and orthocurrence. The loose construction specifies a process in terms of a net of communicating subprocesses; it introduces the notion of a...

For a given pure state of multipartite system, the concurrence vector is defined by employing the defining representation of generators of the corresponding rotation groups. The norm of a concurrence vector is considered as a measure of entanglement. For multipartite pure state, the concurrence vector is regarded as the direct sum of concurrence subvectors in the sense that each subvector is as...

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootters’s concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a “universal inverter,” which acts on quantum systems of...

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootters’s concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a “universal inverter,” which acts on quantum systems of...

We construct a generalized concurrence for general multipartite states based on local W-class and GHZ-class operators. We explicitly construct the corresponding concurrence for three-partite states. The construction of the concurrence is interesting since it is based on local operators.

We study the concurrence of four-qubit quantum states and provide analytical lower bounds of concurrence in terms of the monogamy inequality of concurrence for qubit systems. It is shown that these lower bounds are able to improve the existing bounds and detect entanglement better. The approach is generalized to arbitrary qubit systems.

We study the entanglement of tripartite quantum states and provide analytical lower bound of concurrence in terms of the concurrence of sub-states. The lower bound may improve all the existing lower bounds of concurrence. The approach is generalized to arbitrary dimensional multipartite systems.

The entanglement at zero-temperature is studied in a two-qubit XZ spin-1/2 chain model in anexternal magnetic field which is applied in the z direction. We have obtained an analytical relation forthe effect of the external magnetic field on the concurrence. It is shown that the ground state of thesystem depends on the strength of exchange coupling. We have shown that the analytical relation oft...