Experimental Investigation of the Evolution of Gaussian Quantum Discord in an Open System

Gaussian quantum discord is a measure of quantum correlations in Gaussian systems. Using Gaussian discord, we quantify the quantum correlations of a bipartite entangled state and a separable two-mode mixture of coherent states. We experimentally analyze the effect of noise addition and dissipation on Gaussian discord and show that the former noise degrades the discord, while the latter noise for some states leads to an increase of the discord. In particular, we experimentally demonstrate the near death of discord by noisy evolution and its revival through dissipation.

Figure 1

Experimental setup. See main text for description. Abbreviations: IR: infrared (1064 nm), SH: second harmonic (532 nm), PM and AM: phase and an amplitude electro-optical modulator, OPA: optical parametric amplifier, BS: beam splitter, LO: local oscillator. DAQ/SP: data acquisition/signal processing

Figure 2

(a) Mutual information for the two-mode squeezed state with the circles representing the $I$ information (red) and the $J$ information (blue), measured with the natural logarithm as base (nat). The curves correspond to theoretical curves fitted to the first data point. (b) Quantum discord and logarithmic negativity (inset) for the two-mode state as a function of attenuation. The experimental data (circles) show the discord and logarithmic negativity calculated from the measured covariance matrices, and the solid lines are theoretical fits to the first measurement point (corresponding to a channel attenuation of 0%).

Figure 3

(a) Quantum discord as a function of the modulation depth. The circles represent the experimentally obtained data for discord with 27 dB (green) and 15 dB (blue) common-mode-rejection (CMR) between the homodyne detector at $A$ and the homodyne detecor at $B$. (b) Mutual information $I$ and $J$ as a function of the modulation depth. The circles represent the experimentally obtained data. Solid lines result from theory with perfect detectors (corresponding to a noise-free channel), whereas the dashed and dot-dashed curves are the results of the theory including CMR and electronic noise. The error bars are given by the statistical uncertainties.

Figure 4

The discord of four mixed states from Fig. 3 with different average photon numbers $⟨n⟩$ as a function of attenuation of mode $B$. The error bars are given by the statistical uncertainty. The solid lines are theoretical estimations, fitted to the first data point associated with zero attenuation.

Figure 5

Theoretical simulations of the evolution of Gaussian discord in an attenuating channel for pure two-mode squeezed (TMS) states and two-mode mixtures of coherent states.