ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

242 14. Gaussian entanglement sharing in non-inertial frames
30
GΤΣAR 20
10
0
0
GΤΣAR
P GΤΣAR 0.8
0.6
0.4
0.2
0
1
0
1
r
1
(a)
r
(b)
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Figure 14.2. Bipartite entanglement between Alice and the non-inertial observer
Rob, who moves with uniform acceleration parametrized by the effective
squeezing r. From an inertial perspective, the two observers share a two-mode
squeezed state with squeezing degree s. Plot (a) depicts the Gaussian contangle
Gτ (σA|R), given by Eqs. (6.13, 14.8), as a function of r and s. In plot (b)
the same quantity is normalized to the original contangle as seen by inertial
observers, Gτ (σ p
A|R ) = 4s2 . Notice in (a) how the bipartite Gaussian contangle
is an increasing function of the entanglement, s, while it decreases with
increasing Rob’s acceleration, r, vanishing in the limit r → ∞. This decay is
faster for higher s, as clearly visible in (b).
longer true, as in that case the entanglement between Rob and anti-Rob depends
on s as well. While this is not surprising given the aforementioned inequivalence
between negativities and Gaussian entanglement measures in quantifying quantum
correlation of nonsymmetric mixed Gaussian states [GA7] (see Sec. 4.5), it gives
an indication that the negativity is probably not the best quantifier to capture the
transformation of quantum information due to relativistic effects.
The proper quantification of Gaussian entanglement, shows that the bipartite
quantum correlations are regulated by two competing squeezing degrees. On
one hand, the resource parameter s regulates the entanglement Gτ (σ p
A|R ) = 4s2
measured by inertial observers. On the other hand, the acceleration parameter r
1
1
2
s
2
s
3
3