Mode transformations and entanglement relativity in bipartite Gaussian states

A proper choice of subsystems for a system of identical particles e.g., bosons, is provided by second-quantized modes, i.e., creation/annihilation operators. Here we investigate how the entanglement properties of bipartite Gaussian states of bosons change when modes are changed by means of unitary, number conserving, Bogoliubov transformations. This set of “virtual” bipartitions is then finite-dimensionally parametrized and one can quantitatively address relevant questions such as the determination of the minimal and maximal available entanglement. In particular, we show that in the class of bipartite Gaussian states there are states which remain separable for every possible modes redefinition, while do not exist states which remain entangled for every possible modes redefinition.