ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

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14.3. Distributed Gaussian entanglement due to both accelerated observers 247
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(a)
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Figure 14.5. Total correlations between Alice and the non-inertial observer
Rob, moving with acceleration given by the effective squeezing parameter r.
In an inertial frame the two observers shared a two-mode squeezed state with
squeezing degree s. Plot (a) depicts the evolution of the mutual information
I(σA|R), given by Eq. (14.14), as a function of r and s. In plot (b) the same
quantity is normalized to the entropy of entanglement as perceived by inertial
observers, EV (σ p
), Eq. (14.15). Notice in (a) how the mutual information
A|R
is an increasing function of the initial shared entanglement, s; at variance with
the entanglement (see Fig. 14.2), it saturates to a nonzero value in the limit
of infinite acceleration. From plot (b), one clearly sees that this asymptotic
value is exactly equal to the inertial entropy of entanglement.
of entanglement of Eq. (14.15), meaning that the two parties are correlated both
quantumly and classically to the same degree. When Rob is under acceleration
(r = 0), the entanglement shared with Alice is degraded by the Unruh effect (see
Fig. 14.2), but the classical correlations are left untouched. In the limit r →
∞, all entanglement is destroyed and the remaining mutual information I(σA|R), quantifying classical correlations only, saturates to EV (σ p
A|R ) from Eq. (14.15).
For any s > 0 the mutual information of Eq. (14.14), once normalized by such
entropy of entanglement [see Fig. 14.5(b)], ranges between 2 (1 normalized unit
of entanglement plus 1 normalized unit of classical correlations) at r = 0, and 1
(all classical correlations and zero entanglement) at r → ∞. The same behavior
is found for classical correlations in the case of Alice and Rob sharing a bosonic
two-qubit Bell state in an inertial perspective [88].
14.3. Distributed Gaussian entanglement due to both accelerated observers
A natural question arises whether the mechanism of degradation or, to be precise,
distribution of entanglement due to the Unruh effect is qualitatively modified
according to the number of accelerated observers, or it only depends on the establishment
of some relative acceleration between the observers. One might guess that
when both observers travel with constant acceleration, basically the same features
as unveiled above for the case of a single non-inertial observer will manifest, with
a merely quantitative rescaling of the relevant figures of merit (such as bipartite
entanglement decay rate). Indeed, we will now show that this is not the case [GA20].
We consider here two non-inertial observers, with different names for ease of
clarity and to avoid confusion with the previous picture. Leo and Nadia both travel
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