We study the connection between the Hilbert-Schmidt measure of entanglement (that is the minimal distance of an entangled state to the set of separable states) and entanglement witness in terms of a generalized Bell inequality which distinguishes between entangled and separable states. A method for checking the nearest separable state to a given entangled one is presented. We illustrate the general results by considering isotropic states, in particular 2-qubit and 2-qutrit states -and their generalizations to arbitrary dimensions -where we calculate the optimal entanglement witnesses explicitly.

The influence of the geometric phase, in particular the Berry phase, on an entangled spin-1 2 system is studied. We discuss in detail the case, where the geometric phase is generated only by one part of the Hilbert space. We are able to cancel the effects of the dynamical phase by using the "spin-echo" method. We analyze how the Berry phase affects the Bell angles and the maximal violation of a Bell inequality. Furthermore we suggest an experimental realization of our setup within neutron interferometry.

We study the time evolution of the entangled kaon system by considering the Liouville -von Neumann equation with an additional term which allows for decoherence. We choose as generators of decoherence the projectors to the 2-particle eigenstates of the Hamiltonian. Then we compare this model with the data of the CPLEAR experiment and find in this way an upper bound on the strength λ of the decoherence. We also relate λ to an effective decoherence parameter ζ considered previously in literature. Finally we discuss our model in the light of different measures of entanglement, i.e. the von Neumann entropy S, the entanglement of formation E and the concurrence C, and we relate the decoherence parameter ζ to the loss of entanglement: 1 − E.

We study two different decoherence modes for entangled qubits by considering a Liouville - von Neumann master equation. Mode A is determined by projection operators onto the eigenstates of the Hamiltonian and mode B by projectors onto rotated states. We present solutions for general and for Bell diagonal states and calculate for the later the mixedness and the amount of entanglement given by the concurrence. We propose a realization of the decoherence modes within neutron interferometry by applying fluctuating magnetic fields. An experimental test of the Kraus operator decomposition describing the evolution of the system for each mode is presented.Comment: 15 pages, 5 figure

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