General linear transformations and entangled states

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Abstract
In this paper we study the properties of general linear transformations with complex coefficients, and the effect of such a transformation on a multimode state which is characterized by a Gaussian-Wigner function. We present general results on the changes in the correlation characteristics and the correlation entropy. We then specialize to the two-mode (or two-particle) situation where two-mode squeezed states, subsequently squeezed separately, form a closed set under linear transformations. We derive conditions on the statistical properties of the input fields and the linear transformations such that the state of the output fields is unentangled if the input is unentangled. We present various special cases. Finally, we also discuss the production of entangled states for particles in a harmonic potential.