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arXiv:1405.1754 · Physical Review A

Entanglement sensitivity to signal attenuation and amplification

Sergey N. Filippov, Mário Ziman

Published Jul 2, 2014• 31 citations
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Abstract

Analysis of the noises that accompany attenuation and amplification and impose fundamental limitations on the performance of entanglement-assisted devices shows that Gaussian states of high energy are robust to very asymmetric attenuations, whereas non-Gaussian states are at an advantage in the case of symmetric attenuation and general amplification.

DOI
10.1103/physreva.90.010301

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Analysis of the noises that accompany attenuation and amplification and impose fundamental limitations on the performance of entanglement-assisted devices shows that Gaussian states of high energy are robust to very asymmetric attenuations, whereas non-Gaussian states are at an advantage in the case of symmetric attenuation and general amplification.
Entanglement distribution task encounters a problem of how the initial entangled state should be prepared in order to remain entangled the longest possible time when subjected to local noises. In the realm of continuous-variable states and local Gaussian channels it is tempting to assume that the optimal initial state with the most robust entanglement is Gaussian too; however, this is not the case. Here we prove that specific non-Gaussian two-mode states remain entangled under the effect of deterministic local attenuation or amplification (Gaussian channels with the attenuation factor/power gain κi and the noise parameter μi for modes i=1,2) whenever κ1μ22+κ2μ12<14(κ1+κ2)(1+κ1κ2), which is a strictly larger area of parameters as compared to where Gaussian entanglement is able to tolerate noise. These results shift the “Gaussian world” paradigm in quantum information science (within which solutions to optimization problems involving Gaussian channels are supposed to be attained at Gaussian states).
The recently developed Kraus representation for bosonic Gaussian channels is employed to study analytically the robustness of non-Gaussian entanglement against evolution under noisy attenuator and amplifier environments, and compare it with the robustness of Gaussian entanglement. Our results show that some non-Gaussian states with one ebit of entanglement are more robust than all Gaussian states, even the ones with arbitrarily large entanglement, a conclusion of direct consequence to the recent conjecture by Allegra et al. [Phys. Rev. Lett. 105, 100503 (2010)].
We study general rules of entanglement dynamics for two-mode continuous variable states subjected to deterministic phase-insensitive attenuation and amplification. Since those processes inevitably involve quantum noises, we propose and solve the problem of finding noise levels destroying entanglement of Gaussian and non-Gaussian states. The amplification with power gain greater or equal than 2 necessarily leads to the total loss of entanglement. We consider non-Gaussian states whose entanglement is robust to arbitrary signal attenuation and amplification provided the noise is restricted by some value close to the quantum limited operation. We calculate the lower bound on distillation rate of Bell states.