Dealing with entanglement of continuous variables: Schmidt decomposition with discrete sets of orthogonal functions

Abstract

We propose a method for obtaining the Schmidt decomposition of bipartite systems with continuous variables. It approximates the modes to the prescribed accuracy by well known orthogonal functions. We give some criteria for the control of errors. We illustrate the method comparing its results with the already published analysis for entanglement of biphotons. The agreement is excellent.

6 pages, 4 figures, minor changes, published version