Increasing Entanglement between Gaussian States by Coherent Photon Subtraction

We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states with negative Wigner functions and complex structures more entangled than the initial states in terms of negativity. The experimental results are in very good agreement with the theoretical predictions.

Figure 1

Coherent photon subtraction from Gaussian entangled beams.

Figure 2

Experimental setup.

Figure 3

State separability test after interference between signal and idler beams: (a) joint distribution $P(x_{+},x_{-})$; (b) distributions $P_s(x_{+})$ and $P_c(x_{-})$, for 11 values of $x_{-}$ ($x_{+}$), chosen between $-2$ and $+2$. This separability was verified for several randomly chosen values of ${\theta }_{+}$ and ${\theta }_{-}$ (here ${\theta }_{+}=20°$ and ${\theta }_{-}=50°$).

Figure 4

(a) Set of experimentally measured quadrature distributions (dots), compared to those reconstructed from our model (solid line). (b) Wigner function corrected for homodyne detection losses, obtained with a standard maximal-likelihood algorithm (MaxLike), compared to the result of our model. This state is produced with 1.8 dB of squeezing and $R=5\%$.

Figure 5

Tomography of two states produced with 1.3 dB (first row) and 3.2 dB (second row) of squeezing and $R=10\%$: three different cuts of the two-mode Wigner function.

Figure 6

Entanglement negativity of the initial and final states as a function of squeezing for several pickoff BS reflectivities, corrected for homodyne detection losses. Solid lines are theoretical calculations using the average values of the experimental parameters.