Mode-Wise Entanglement of Gaussian States

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  • 3 September 2002
Abstract
We investigate the decomposition of a multi-mode pure Gaussian state with respect to a bi-partite division of the modes. It is shown that for any such division the state can always be expressed as a product state involving entangled two-mode squeezed states and single mode local states at each side. The character of entanglement of the state can therefore be understood mode-wise; that is, a given mode on one side is entangled with only one corresponding mode of the other, and therefore the total bi-partite entanglement is the sum of the mode-wise entanglement. This result can be linked to a general decomposition property of a certain class of "isotropic" CMs, the symplectic spectrum of which is completely degenerate, and thus to a more general mode-wise decomposition of a restricted class of Gaussian mixed states.

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