ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

12.2. Equivalence between entanglement and optimal teleportation fidelity 203
opt
optimal fidelity N
multiuser fidelityN
1
0.9
0.8
0.7
0.6
0.5
1
0.9
0.8
0.7
0.6
0.5
2
0.73
0.728
0.726
0.724
0.722
0.72
4.9 4.95 5 5.05 5.1
0 5 10 15 20
average squeezing r dB
2
3
4
3
4
(a)
8 20
50
(b)
8
20
50
optimal
unbiased
eq.sqz.
0 5 10 15 20
squeezing r1r2r dB
Figure 12.3. (a) Optimal fidelity for teleporting unknown coherent states
from any sender to any receiver chosen from N (= 2, 3, 4, 8, 20, and 50) parties,
sharing pure N-party entangled symmetric Gaussian resources and with the
aid of N −2 cooperating parties, plotted as a function of the average squeezing
used in the resource production (expressed in decibels, for the definition of dB
see footnote 20 on page 144). The optimal fidelity is nonclassical (F opt >
F cl ≡ 0.5) for any N, if the initial squeezings are adjusted as in Eq. (12.24)
[GA9]. At fixed entanglement, states produced with all equal squeezers yield
lower-than-classical fidelities (F < F cl ≡ 0.5) for N ≥ 30, as shown in (b)
(adapted from Fig. 1 of Ref. [236]). In the inset of Plot (a) we compare, for
N = 3 and a window of average squeezing, the optimal fidelity (blue solid
line), the fidelity obtained with states having all unbiased quadratures [32]
(green dashed line), and the fidelity obtained with equally squeezed states
[236] (red dotted line). The three curves are close to each other, but the
optimal preparation yields always the highest fidelity.
as ¯r > 0 for any N, in which case the considered class of pure states is genuinely
multiparty entangled (we have shown this unambiguously in Sec. 5.2). Therefore,
we can state the following [GA9].