2 research outputs found
Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition
In a previous paper we examined a geometric measure of entanglement based on
the minimum distance between the entangled target state of interest and the
space of unnormalized product states. Here we present a detailed study of this
entanglement measure for target states with a large degree of symmetry. We
obtain analytic solutions for the extrema of the distance function and solve
for the Hessian to show that, up to the action of trivial symmetries, the
solutions correspond to local minima of the distance function. In addition, we
show that the conditions that determine the extremal solutions for general
target states can be obtained directly by parametrizing the product states via
their Schmidt decomposition.Comment: 16 pages, references added and discussion expande
Evolution of entanglement entropy in one-dimensional systems
We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the Hamiltonian. We use path integral methods of quantum field theory as well as explicit computations for the transverse Ising spin chain. In both cases, there is a maximum speed v of propagation of signals. In general the entanglement entropy increases linearly with time t up to t = l/2v, after which it saturates at a value proportional to l, the coefficient depending on the initial state. This behaviour may be understood as a consequence of causality