Gaussian local unitary equivalence ofn-mode Gaussian states and Gaussian transformations by local operations with classical communication

Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations

Gerardo Adesso, Salvatore M. Giampaolo, and Fabrizio Illuminati* Dipartimento di Fisica “E. R. Caianiello,” Università degli Studi di Salerno, Via S. Allende, I-84081 Baronissi (SA), Salerno, Italy CNR-INFM Coherentia, Napoli, Italy; CNISM, Unità di Salerno, Salerno, Italy; and INFN, Sezione di Napoli-Gruppo Collegato di Salerno, Salerno, Italy Grup d’Informació Quàntica, Universitat Autónoma d...

Expected Number of Local Maxima of Some Gaussian Random Polnomials

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-s...

Distilling Gaussian states with Gaussian operations is impossible.

We show that no distillation protocol for Gaussian quantum states exists that relies on (i) arbitrary local unitary operations that preserve the Gaussian character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local Gaussian unitary operations on two symmetric identically prepared copies. This is in contrast to the finite-dimension...

Gaussian sampling by local perturbations

We present a technique for exact simulation of Gaussian Markov random fields (GMRFs), which can be interpreted as locally injecting noise to each Gaussian factor independently, followed by computing the mean/mode of the perturbed GMRF. Coupled with standard iterative techniques for the solution of symmetric positive definite systems, this yields a very efficient sampling algorithm with essentia...