Abstract

We reexamine the interpretation of negativity of a generally mixed two-mode Gaussian state by diagonalizing ρ^TA (the partial transposition of density matrix ρ) directly. We show that negativity can be explicitly expressed in terms of an optimal uncertainty product corresponding to the greatest violation of a separability criterion based on positive partial transposition [1], In addition, the explicit form of the eigenvectors of ρ^ta provides a way to construct entanglement witness operators [2]. We apply our analysis of negativity to disentanglement dynamics in two physical situations in optics. First, we study two-mode squeezed states interacting with symmetric linear baths. Second, we study the decoherence of hyper-entangled two-photon states due to polarization mode dispersion in optical fibers. In both problems, we present the time-dependence of negativity and indicate how the disentanglement times depend on system parameters.

© 2008 Optical Society of America