Quantum Key Distillation from Gaussian States by Gaussian Operations

Abstract

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.

Efficiency in Quantum Key Distribution Protocols with Entangled Gaussian States

“…Notice that Eve can gain information if the overlap between her states after Alice and Bob have measured coincident results is sufficiently small. The above inequalities come from the fact that in the case of individual attacks the error on Eve's estimation of the final bit b is bound from below by a term proportional to | e ++ |e −− | N [1]. Therefore, Alice and Bob can establish a key if…”

“…In [1] it was shown that any 1 × 1 NPPT state fulfills the above inequality and thus any NPPT gaussian state can be used to establish a secure key in front of individual eavesdropper attacks.…”

“…First, we summarize the main steps of the protocol used in [1]. Without loosing generality, and by virtue of the properties of gaussian states, one should only consider the case in which Alice and Bob share many copies of a quantum system of 1 × 1 symmetric NPPT gaussian stateρ AB .…”

“…In Sect. 3, we first review the previous protocol [1] and present our new results. Finally, we present our conclusions in Sect.…”

“…The superiority of quantum cryptography comes from the fact that the laws of quantum mechanics permit to the legitimate users (Alice and Bob) to infer if an eavesdropper has monitored the distribution of the key and has gained information about it. If this is the case, Alice and Bob will both agree in protocol is based on output coincidences of the measurements of the quadratures which, by definition, are operators with a continuous spectrum, the protocol has zero efficiency [1].…”