ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

224 13. Entanglement in Gaussian valence bond states
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Figure 13.3. Entanglement properties of the three-mode building block γ,
Eq. (13.1), of the Gaussian valence bond construction, as functions of the
standard form covariances x and d ≡ s − smin. (a) Bipartite entanglement,
as quantified by the logarithmic negativity, between the first two input-port
modes 1 and 2; (b) Bipartite entanglement, as quantified by the logarithmic
negativity, between each of the first two modes and the output-port mode 3;
(c) Genuine tripartite entanglement, as quantified by the residual Gaussian
contangle, among all the three modes.
third one γ x decreases with s. One can also show that the genuine tripartite entanglement
in the building block, as quantified by the residual Gaussian contangle
Eq. (7.36) (see Sec. 7.2.3), increases both as a function of x and with increasing
difference
d ≡ s − smin . (13.6)
The bipartite and tripartite entanglement properties of the building block are summarized
in Fig. 13.3.
13.2. Entanglement distribution in Gaussian valence bond states
The main question we raise is how the initial entanglement in the building block γ
gets distributed in the GVBS Γ out . The answer will be that the more entanglement
we prepare in the input port γ ss, the longer the range of the quantum correlations
in the output GVBS will be [GA13]. We start from the case of minimum s.
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