ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

252 14. Gaussian entanglement sharing in non-inertial frames
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Figure 14.8. Bipartite entanglement between the two non-inertial observers
Leo and Nadia, both traveling with uniform acceleration given by the effective
squeezing parameter a. From an inertial perspective the two observers
share a two-mode squeezed state with squeezing degree s. Plot (a) depicts the
Gaussian contangle Gτ (σL|N ), given by Eqs. (6.13, 14.26), as a function of
a and s. In plot (b) the same quantity is normalized to the contangle in the
Minkowski frame, Gτ (σ p
L|N ) = 4s2 . Notice in (a) how the bipartite Gaussian
contangle is an increasing function of the inertial entanglement, s, while it
decreases with increasing acceleration, a. This decay is faster for higher s, as
clearly visible in (b). At variance with the case of only one accelerated observer
(Fig. 14.2), in this case the bipartite entanglement can be completely destroyed
at finite acceleration. The black line depicts the threshold acceleration a∗ (s),
Eq. (14.25), such that for a ≥ a∗ (s) the bipartite entanglement shared by the
two non-inertial observers is exactly zero.
14.3.1.2. Equal acceleration parameters. We return to consider detectors sensitive to
a single mode frequency and, for simplicity, we restrict our attention to the case
where Leo and Nadia’s trajectories have the same acceleration parameter
l = n ≡ a . (14.24)
This means that λ/aL = ν/aN. While the following results do not rely on this
assumption, it is particularly useful in order to provide a pictorial representation
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