We extend the concept of negativity, a good measure of entanglement for bipartite pure states, to mixed states by means of the convex-roof extension. We show that the measure does not increase under local quantum operations and classical communication, and derive explicit formulas for the entanglement measure of isotropic states and Werner states, applying the formalism presented by Vollbrecht and Werner [Phys. Rev. A 64, 062307 (2001)].

We study entanglement of electron spins in many-body systems based on the Green’s function approach. As an application we obtain the two-particle density matrix of a noninteracting electron gas and identify its two-spin density matrix as a Werner state. We calculate entanglement measures, a classical correlation, mutual information, and a pair-distribution function of two electrons at zero and finite temperatures. We find that changes of entanglement measures are proportional to $T^2$ at low temperatures.

We study a system of two qubits interacting with a common environment, described by a two-spin boson model. We demonstrate two competing roles of the environment: inducing entanglement between the two qubits and making them decoherent. For the environment of a single harmonic oscillator, if its frequency is commensurate with the induced two-qubit coupling strength, the two qubits could be maximally entangled and the environment could be separable. In the case of the environment of a bosonic bath, the gap of its spectral density function is essential to generate entanglement between two qubits at equilibrium and for it to be used as a quantum data bus.

We derive exact time evolution of three two-level atoms coupled to a common environment. The environment is structured and is modeled by a leaky cavity with Lorentzian spectral density. The atoms are initially prepared in a generalized $W$ state and later on experience pairwise dipole-dipole interactions and couplings to the cavity. We study tripartite disentangling and entangling dynamics as well as protecting bipartite entanglement with both atom-atom interactions and atom-cavity couplings taken simultaneously into account. DOI: http://dx.doi.org/10.1103/PhysRevA.84.022329 ©2011 American Physical Society

We study exact entanglement dynamics of three-qubit W-class states in a common structured cavity at zero temperature in both Markovian and non-Markovian regimes using the concept of lower bound of concurrence. We also propose three methods to control the qubits' entanglement evolution and establish monogamy equalities relevant to the class of states under consideration.