Experimental Demonstration of Continuous Variable Cloning with Phase-Conjugate Inputs

We report the first experimental demonstration of continuous variable cloning of phase-conjugate coherent states as proposed by Cerf and Iblisdir [Phys. Rev. Lett. 87, 247903 (2001)]. In contrast to this proposal, the cloning transformation is accomplished using only linear optical components, homodyne detection, and feedforward. As a result of combining phase conjugation with a joint measurement strategy, superior cloning is demonstrated with cloning fidelities reaching 89%.

Figure 1

Proposed setup for an $N+N\to M$ cloning machine. $\mathrm{BS}(T)$: Variable beam splitter with transmission $T$ and reflection $R$. ${\mathrm{HD}}_{x(p)}$: Homodyne detector measuring $x(p)$. $g_1$, $g_{2x}$, and $g_{2p}$: Electronic gains. $D(x,p)$: Displacers of $x$ and $p$. EPR: Einstein-Podolsky-Rosen entanglement source. $v_i$ denotes the vacuum inputs while ${\rho }_i$ denotes the density operators of the outputs.

Figure 2

Schematic of the experimental setup. AM: amplitude modulator; PM: phase modulator; $g$: electronic gains. ${\rho }_1$, ${\rho }_2$, and ${\rho }_3$ are the density operators of the clones.

Figure 3

Spectral noise powers relative to the shot noise for the two clones. Red (light gray) and blue (dark gray) traces correspond to the added cloning noise with respect to the input state for the phase and amplitude quadrature, respectively. The $1\to 2$, $1+1\to 2$, and $2\to 2$ cloning limits are illustrated by solid straight lines at the 3, 0.5, and 0 dB levels. The data were corrected taking into account the homodyne detection efficiencies which were measured to be 83% and 85% for clones 1 and 2. The noises were measured to ${\Delta }^2{x}_1=1.15\pm 0.2$ and ${\Delta }^2{p}_1=1.18\pm 0.2$ for clone 1, and ${\Delta }^2{x}_2=1.19\pm 0.2$ and ${\Delta }^2{p}_2=1.19\pm 0.2$ for clone 2. The optical gains for this particular measurement run were $G_{p1}=1.01\pm 0.01$, $G_{x1}=1.02\pm 0.01$, $G_{p2}=1.00\pm 0.01$, and $G_{x2}=0.99\pm 0.01$. Video bandwidth 30 Hz and sweep time 2 sec.

Figure 4

Spectral noise powers relative to the shot noise for the three clones. The straight lines at the 1.25 and 0.87 dB level represent the optimal limits for $2\to 3$ and $1+1\to 3$ cloning, respectively. The data were corrected taking into account the homodyne detection efficiencies which were measured to be 83%, 85%, and 80% for clones 1, 2, and 3. For this particular measurement run we measured the following noises: ${\Delta }^2{x}_1=1.26\pm 0.2$, ${\Delta }^2{p}_1=1.27\pm 0.2$, ${\Delta }^2{x}_2=1.22\pm 0.2$, ${\Delta }^2{p}_2=1.28\pm 0.2$, ${\Delta }^2{x}_3=1.23\pm 0.2$, and ${\Delta }^2{p}_3=1.28\pm 0.2$; and the following gains: $G_{p1}=1.00\pm 0.01$, $G_{x1}=0.95\pm 0.01$, $G_{p2}=0.95\pm 0.01$, $G_{x2}=0.96\pm 0.01$, $G_{p3}=1.01\pm 0.01$, and $G_{x3}=1.00\pm 0.01$.