Fig. 1. (a) Principle of the test of EDR with continuous variables. A joint measurement apparatus implements the approximations of incompatible observables A and B with the compatible observables C and D by coupling the signal and meter modes via a beam-splitter. Coherent state (CS), squeezed state (SS), and thermal state (TS) serve as signal modes, and a vacuum state serves as meter mode. (b) Schematic of the experimental setup. Signal state is prepared by a NOPA. The measurement apparatus is composed by a BS, which is a combination of PBS–HWP–PBS, and two HDs. Two output modes of the BS are detected by HD1 and HD2, respectively. NOPA, nondegenerate optical parametric amplifier; BS, beam-splitter; HWP, half-waveplate; PBS, polarization beam-splitter; HD, homodyne detector; LO, local oscillator.

Fig. 2. Experimental results. (a), (b) and (c) Dependence of error (black curve) and disturbance (red curve) on the transmission efficiency of BS (T) for coherent, squeezed, and thermal states, respectively. (d), (e) and (f) Lefthand sides of the EDRs with continuous variables for coherent, squeezed, and thermal states, respectively. Green curve, Heisenberg’s EDR; red curve, Ozawa’s EDR; blue curve, Branciard’s EDR. Black line, righthand side of the EDR. All experimental data agree well with the theoretical predictions. The error bars are obtained by RMS of measurements repeated ten times.

Fig. 3. Comparison of the lower bounds of EDRs for three Gaussian states. (a) Coherent state as signal mode. (b) Squeezed state as signal mode. (c) Thermal state as signal mode. Blue curve, Heisenberg bound; orange curve, Ozawa bound; green curve, Branciard bound. Black circles show experimental data. Black dotted curve shows the theoretical prediction for the experimental parameters.