Entanglement and Area Laws in Weakly Correlated States

MATERA, JUAN MAURICIO; ROSSIGNOLI, RAUL; CANOSA, NORMA

Paraty

Congreso; IV Paraty Quantum Information School and Workshop; 2013

Here we will discuss the evaluation of entanglement measures in weakly correlated gaussian states. It will be shown how they can be expressed in terms of the singular values of a particular block of the generalized contraction matrix. This result enables to obtain in a simple way asymptotic expressions and related area laws for the entanglement entropy of bipartitions in pure states, as well as for the logarithmic negativity associated with bipartitions and also pairs of arbitrary subsystems. As an illustration, we consider different types of contiguous and noncontiguous blocks in two dimensional lattices. Exact asymptotic expressions are provided for first neighbor couplings, which lead to area laws depending on the orientation and separation of the blocks.