Unconditional Quantum Cloning of Coherent States with Linear Optics

A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the presented scheme is limited only by detection inefficiencies. Experimentally, we achieved a cloning fidelity of about 65%, which almost touches the optimal value of $2/3$.

Figure 1

Schematic drawing showing the principle of the continuous variable cloning scheme using only linear optics and homodyne detection. $v_1$, $v_2$, and $v_3$ are vacuum inputs; $D$ is a displacement governed by the measurement $\alpha$ scaled with the gain $\lambda$.

Figure 2

Schematic of the CV cloning setup divided into three boxes defining the preparation stage (where an arbitrary input coherent state can be generated), the cloning stage (where two clones are produced), and the verification stage (where the quality of the cloning process is quantified). BS, beam splitter; $\lambda$, electronic gain; LO, local oscillator; AM, amplitude modulator; PM, phase modulator; AUX, auxiliary beam.

Figure 3

Spectral densities for the input state [traces (ii)] and the output clones [traces (iii)], 1 and 2, of the Gaussian cloning machine, measured by the two homodyne detection systems in a 2 MHz span mode and a center frequency of 14.3 MHz corresponding to the location of the sidebands. The traces are normalized to the quantum noise limit [traces (i)]. Resolution bandwidth is 100 kHz and video bandwidth is 30 Hz. (a) and (b) show the spectra for the amplitude and the phase quadratures of clone 1 and similarly (c) and (d) the spectra for clone 2. Since the input signal was measured with the same homodyne detectors as the output clones, the measurement of the input signal is degraded by the two $50/50$ beam splitters BS1 and BS3 and unity cloning gain is ensured by a 6 dB difference between the input signal and the clones.

Figure 4

Spectral noise densities of the clones relative to the quantum noise level (lower black trace) recorded by the homodyne detectors both for the amplitude quadrature [red (grey) trace] and for the phase quadrature [blue (upper dark) trace]. The added noise contributions are $3.28\pm 0.13\mathrm{dB}$ ($3.16\pm 0.13\mathrm{dB}$) and $3.20\pm 0.11\mathrm{dB}$ ($3.15\pm 0.13\mathrm{dB}$) in the amplitude quadrature and phase quadrature of clone 1 (2). The optimal cloning limit as well as the classical limit are shown by solid lines. The measurement frequency is 14.3 MHz, the sweep time 2 s, the resolution bandwidth 100 kHz, and the video bandwidth 300 Hz. On the right-hand side, we plot the associated noise contours of the Wigner functions corresponding to the input state [green (dark grey) contour], the experimentally achieved clones [light blue (light grey) contour] and the classical clones (dashed line).