Simple proof of the robustness of Gaussian entanglement in bosonic noisy channels

Abstract

The extremality of Gaussian states is exploited to show that Gaussian states are the most robust, among all possible bipartite continuous-variable states at fixed energy, against disentanglement due to noisy evolutions in Markovian Gaussian channels involving dissipation and thermal hopping. This proves a conjecture raised recently [M. Allegra, P. Giorda, and M. G. A. Paris, Phys. Rev. Lett. 105, 100503 (2010)], providing a rigorous validation of the conclusions of that work. The problem of identifying continuous-variable states with maximum resilience to entanglement damping in more general bosonic open-system dynamical evolutions, possibly including correlated noise and non-Markovian effects, remains open.Continuous-variable (CV) systems such as light modes and ultracold atomic ensembles [1] provide advantageous resources to achieve unconditional implementations of quantum information processing [2], ranging from teleportation protocols [3] to quantum key distribution [4] and one-way quantum computation [5]. Gaussian states and Gaussian operations, which represent respectively the most natural and easily controllable light states as well as the set of manipulations efficiently realizable by linear optics, have traditionally occupied a privileged role in all such implementations. Furthermore, by virtue of their mathematical simplicity compared to general states living in infinite-dimensional Hilbert spaces, bosonic Gaussian states have been and are the preferred testing grounds for a broad variety of investigations into the structure, nature, and dynamics of CV entanglement and quantum correlations [6].However, some prominent limitations of a Gaussian-only toolbox have been recently exposed in several contexts [7], stimulating vigorous theoretical and experimental research into the realm of non-Gaussian-state engineering and characterization [8], to assess and harness the potentially enhanced performance of de-Gaussified CV resources for quantum teleportation [9], entanglement distillation [10], parameter estimation [11], universal quantum computation [5,12], nonlocality tests [13], and so forth. Still, one of the most powerful features of Gaussian quantum states is their extremality [14] in the space of all CV states, which allows us to formulate valuable bounds on suitable entanglement measures and entropic degrees for a general non-Gaussian state , based on the corresponding (easier to compute) properties of the Gaussian state σ with the same first and second statistical moments as . This has important consequences for the security of CV quantum key distribution [15].The transmission of one-mode and multimode, possibly entangled, beams between distant locations, a basic necessity for the realization of a distributed quantum communication network [16], is unavoidably affected by various types of noise. While phase diffusion (dephasing) dampens the coherences in the Fock basis, transforming Gaussian states into non-Gaussian ones, the exposition to dissipative losses and thermal hopping yields an instance of a G...

Quantifying non-Gaussianity of quantum-state correlation

“…Furthermore, non-Gaussian resources provide advantages over Gaussian counterparts. Non-Gaussian entanglement can be more robust against Gaussian noises than Gaussian entanglement [11][12][13][14][15][16][17]. Non-Gaussian states can be distilled by Gaussian operations to increase squeezing [18][19][20] and entanglement [21,22].…”

Entanglement distillation for continuous variables in a thermal environment: Effectiveness of a non-Gaussian operation

“…On the other hand, when the strength of thermal noise becomes rather significant, the Gaussian entanglement dies out at a certain value of interaction time [Eq. (15)]. For example, the initial Gaussian entanglement disappears at η ∼ 0.8 in Fig.…”

Rényi formulation of entanglement criteria for continuous variables

“…Inequalities converse to (20) generally involve indices, some of which are negative. Here, the definition should be reformulated.…”

“…Properties of Gaussian entanglement with respect to information processing were discussed in [18][19][20][21]. Entanglement criteria of the second-order type deal with variations of certain observables.…”