Entanglement and interface conditions on fields

We consider the vacuum wave function of a free scalar field theory in space partitioned into two regions, with the field obeying Robin conditions (of parameter <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>κ</a:mi></a:mrow></a:math>) on the interface. A direct integration over fields in a subregion is carried out to obtain the reduced density matrix. This leads to a constructive proof of the Reeh-Schlieder theorem. We analyze the entanglement entropy as a function of the Robin parameter <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>κ</c:mi></c:math>. We also consider a specific conditional probability as another measure of entanglement which is more amenable to analysis of the dependence on interface conditions. Finally, we discuss a direct calculation of correlation functions and how it gives an alternate route to the reduced density matrix.