Quantum Key Distillation from Gaussian States by Gaussian Operations

We study the secrecy properties of Gaussian states under Gaussian operations. Although such operations are useless for quantum distillation, we prove that it is possible to distill a secret key secure against any attack from sufficiently entangled Gaussian states with nonpositive partial transposition. Moreover, all such states allow for key distillation, when Eve is assumed to perform finite-size coherent attacks before the reconciliation process.

Figure 1

Security analysis of symmetric $1\times 1$ Gaussian states when $c_x=c_p=c$. All physical states are above the solid line. The dashed line defines the entanglement limit, which coincides with the security bound against incoherent attacks. States below the dotted line are secure against any attack.

Figure 2

Schematic representation of quantum and classical key distillation techniques from quantum states. In this work, Alice and Bob perform only Gaussian operations.