Gaussian states and Gaussian transformations represent an interesting counterpart to two-level systems in quantum optics, on the one hand easily described using first and second moments of quadrature operators and on the other hand simple to implement experimentally using linear optics and optical parametric amplifiers. Here, we propose and analyse protocols for manipulation of entangled Gaussian states of light using local operations and classical communication. Firstly, we study entanglement concentration based on photon subtraction enhanced by local coherent displacements for states in the form of a single-mode squeezed vacuum state split on a beam splitter. We show that coherent displacements can enhance entanglement concentration based on photon subtraction. Secondly, we study transformations of multipartite permutation invariant Gaussian states. We investigate how entanglement classification is changed by these transformations. In addition, as a figure of merit characterising the quality of the entanglement, we use fidelity of assisted quantum teleportation. We study two different strategies to achieve this objective. The first one is based on adding correlated noise to each mode while the other employs partial non-demolition measurements.

1. Transformations of continuous-variable entangled states of light
Ond ej ernotík1,2,3
and Jaromír Fiurášek1
1
Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
2
Institute for Theoretical Physics, Leibniz University Hannover, Appelstraße 2, 30167 Hannover, Germany
3
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Callinstraße 38, 30167 Hannover, Germany
Motivation
Gaussian states are interesting to both theorists and
experimentalists for the ease of their mathematical
description and simple experimental manipulation.
While they are powerful, open questions still persist.
E.g., multipartite entanglement (below, Ref. [1]) is
still mostly an unexplored issue. In addition,
Gaussian states are not universal. Some tasks, such
as entanglement concentration of Gaussian states
(right, Ref. [2]) require non-Gaussian operations in
order to succeed.
Acknowledgements
This work was supported by the Czech Science Foundation under
projects P205/12/0577, P205/12/0694 and by the Palacký
University through grants PrF-2012-019, PrF-2013-008.
Single mode subtraction
In the weak squeezing limit (considering only
vacuum and two-photon contributions), the filtered
state is , giving maximally
entangled state for zero displacement and
a balanced beam splitter.
With arbitrary squeezing, we consider a realistic
scenario with single-photon detectors with limited
detection efficiency and finite transmittance of tap-
off beam splitters. For single-mode subtraction, zero
displacement still appears to be optimal.